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Basic Characteristics of Yield of Materials under Complex Stress

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Generalized Plasticity

Summary

Some characteristics of yield of materials under complex stresses are discussed in this chapter. They are the SD effect, the effect of hydrostatic stress, the effect of normal stress, the effect of intermediate principal stress, the effect of intermediate principal shear-stress, symmetry and the convexity of yield surfaces. The research on the SD effect, the effect of hydrostatic stress and the effect of normal stress have developed rapidly because they can easily be carried out with relatively ordinary experimental facilities, and can be explained by theory on hand. However, research on the effect of intermediate principal stress has been more difficult and time-consuming. This is because its experiments are difficult, and it requires more accurate as well as more expensive facilities. Research on the effect of the intermediate principal stress and the effect of intermediate principal shear-stress will have to continue, and has become an interesting as well as significant topic for scholars.

Strength theory deals with the yield of materials under the complex stress state. It is difficult to find a general law for the varieties of yield of materials under the complex stress. However, considerable experimental and theoretical studies have provided us with valuable data for comparison, verification and study of the avaiable criteria.

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References

  • Bishop AW (1966) The strength of soils as engineering materials. Sixth Rankine Lecture, Geotechnique, 16(2), 89–128.

    MathSciNet  Google Scholar 

  • Bishop AW (1971) Shear strength parameters for undisturbed and remoulded soil specimens. Stress-Strain Behaviour of Soils Proc. (Roscoe Memorial Symposium, Cambridge University, Cambridge, England 1971), Parry RHG ed. Foulis, pp 1–59.

    Google Scholar 

  • Bridgman PW (1964) Studies in Large Plastic Flow and Fracture, with Special Emphasis on the effects of Hydrostatic Pressure. Harvard University Press, Cambridge.

    Google Scholar 

  • Byerlee JD (1967a) Theory of friction based on brittle fracture. J. Appl. Phys. 38, 2928–34.

    Article  Google Scholar 

  • Byerlee JD (1967b) Frictional characteristics of grahite under high confining pressure. J. Geophys. Res. 72, 3639–48.

    Article  Google Scholar 

  • Byerlee JD (1970) Static and kinetic friction of granite at high normal stress. Int. J. Rock Mech. Min. Sci. and Geomech. Abstrs 7, 577–582.

    Article  Google Scholar 

  • Butterfield R and Harkness RM (1971) The kinematics of Mohr—Coulomb materials. Stress-Strain Behaviour of Soils. Parry RHG ed. Foulis, pp 220–233.

    Google Scholar 

  • Chait R (1972) Factors influencing the strength differential of high strength steels. Metallurgical Transactions 3, 365–371.

    Google Scholar 

  • Cornforth DH (1964) Some experiments on influence of strain conditions on the strength of sand. Geotechnique 143–167.

    Google Scholar 

  • Drucker DC (1973) Plasticity theory, strength differential (SD) phenemenon, and volume expansion in metals and plastics. Metall. Trans. 4, 667–673.

    Google Scholar 

  • Ergun MU (1981) Evaluation of three-dimensional shear testing. Proc. of 10th Int. Conf. on Soil Mechanics and Foundation Engng, Stockholm, 593–596.

    Google Scholar 

  • Finn WD and Mittal HK (1963) Shear strength of soil in a general stress space. ASTM STP no. 361. Laboratory shear testing of soils. 42–48.

    Google Scholar 

  • Goodman R.E (1980) Introduction to Rock Mechanics. John Wiley and Sons, New York.

    Google Scholar 

  • Green GE (1972) Strength and deformation of sand measured in an independent stress control Cell. Roscoe memorial Symposium’ stress-strain behaviour of soils’. G.T. Foulis and Co. 285–323.

    Google Scholar 

  • Green GE and Bishop AW (1969) A note on the drained strength of sand under generalized strain conditions. Geotechnique, 19(1), 144–149.

    Article  Google Scholar 

  • Hanbly, E.C. and Roscoe, K.H. (1969) Observations and predictions of stresses and strains during plane strain of wet clays. Proc. 7th Int. Conf, Soil Mech. Found. Engg.(1), 173 181.

    Google Scholar 

  • Handin J, Heard HC and Magouirk JN (1967) Effect of the intermediate principal stress on the failure of limestone, dolomite and glass at different temperatures and strain rates. J. Geophys. Res. 72, 611–640.

    Google Scholar 

  • Hobbs DW (1966) A study of the behaviour of a broken rock under triaxial compression, and its application to mine roadways. Int. J. Rock Mech. Min. Sci. 3, 11–43.

    Article  Google Scholar 

  • Hoskins ER, Jaeger JC, and Rosengren KJ (1968) A medium scale direct friction experiment, Int. J. Rock Mech. Min. Sci., 5, 143–154.

    Article  Google Scholar 

  • Hoskins ER (1969) The failure of thick-walled hollow cylinders of isotropic rock. Int. J. Rock Mech. Min. Sci., 6, 99–125.

    Article  Google Scholar 

  • Ichibara M. and Matsuzawa H (1973) Application of plane strain tests to earth pressure. Proc. 8th Int. conf. Soil Mech. Found. Engg.(1.1), 185–190. Moscow.

    Google Scholar 

  • Jaeger JC (1963) Extension failures in rocks subject to fluid pressure, J. Geophys. Res.,68, 6066–6067.

    Google Scholar 

  • Jaeger JC and Hoskins ER (1966), Rock failure under the confined Brazilian test, J. Geophys. Res., 71-2651–2659.

    Google Scholar 

  • Jaeger JC and Cook NGW (1979) Fundamentals of Rock Mechanics. 3rd. Chapman and Hall, London.

    Google Scholar 

  • Kwagniewski. M., Takahashi, M. & Li. X (2003) Volume changes in sandstone under true triaxial compression conditions. In: ISRM 2003-Technology roadmap for rock mechanics, South African Institute of Mining and Metallurgy. 683–688

    Google Scholar 

  • Ko HY and Scott RF (1967) Deformation of sand in shear. J. of Soil Mechanics and Foundations 93, 283–310.

    Google Scholar 

  • Ko HY and Scott RF (1968) Deformation of sand at failure. J. of Soil Mechanics and Foundations 94, 883–898.

    Google Scholar 

  • Lade, P.V. and Duncan J.M. (1973). Cubical triaxial tests on cohesionless soil. ASCE J.Soil Mech. and Found. Div. No.lO, 793–812.

    Google Scholar 

  • Launay P and Gachon H (1971) Strain and ultimate strength of concrete under triaxial stress. Proc. 1st Int. Conf. Struc. Mech. Reactor Technol., Belin, paper H1/3.

    Google Scholar 

  • Lee KL (1970) Comparison of plane strain and triaxial tests on sand. ASCE J. Soil Mech. And Found. Div. No. 3, 901–923.

    Google Scholar 

  • Leussink H and Wittke w (1963). Difference in triaxial and plane strain shear strength. ASTM STP No. 361 Laboratory shear testing of soils. 77–89.

    Google Scholar 

  • Lewandowski JJ and Lowhaphandu P (1998) Effects of hydrostatic pressure on mechanical behaviour and deformation processing of materials. Int. Materials Reviews 43(4), 145–187.

    Google Scholar 

  • Mansfield EH (1971) Biaxial yield criteria. J. of the Royal Aeronautical Society 75(732), 849–850.

    Google Scholar 

  • Matsuoka H and Nakai T (1974) Stress-deformation and strength characteristics of soil under three different principal stresses. Proc. of Japan Society of Civil Engineers 232, 59–70.

    Google Scholar 

  • Matsuoka H and Nakai T (1985) Relationship among Tresca, Mises, Mohr—Coulomb and Matsuoka—Nakai failure criteria. Soils and Foundations (Japan) 25(4), 123–128.

    Google Scholar 

  • Michelis P (1985) Polyaxial yielding of granular rock. J. Eng. Mech. 111, 1049–1066.

    Article  Google Scholar 

  • Michelis P (1985) True triaxial cycle behavior of concrete and rock in compression. Int. J. of Plasticity, 3(2), 249–270.

    Google Scholar 

  • NagaraJ, T.S. and Somashekar, B.V. (1979) stress deformation and strength of soils in plane strain. VI Asian Reg. Conf. on Soll Mech. and Found. Engg. (I), 43–46

    Google Scholar 

  • Parry RHG (1971) A study of influence of intermediate principal stress on Ï• values using a critical state theory.IV ARC on Soll Mech.Found.Enggo(1),159–165, Bangkok.

    Google Scholar 

  • Ramamurthy T and Tokhi VK (1981) Relation of triaxial and plane strain strength. Proceedings of 10th Int. Conf. on Soil Mech. and Fund. Engrg., Stockholm, pp 755–758.

    Google Scholar 

  • Rauch GC and Leslie WC (1972) The extent and nature of the strength-differential effect in steels. Metallurgical Transactions 3, 373–381.

    Google Scholar 

  • Rawat PC (1976) Shear behaviour of cohesionless materials under generalized conditions of stress and strain. P h.D. thesis, IoIoT. DeLhi, 415 pp.

    Google Scholar 

  • Reades DW (1972) Stress-strain characteristics of a sand under three dimensional oading. Ph.D. thesis, Uni of London.

    Google Scholar 

  • Richmond O and Spitzig WA (1980) Pressure dependence and dilatancy of plastic flow. Theoretical and Applied Mechanics, 15th ICTAM, pp 377–386.

    Google Scholar 

  • Rowe PW(1962) The stress-dilatancy relationship for static equilibrium of an asse∼bly of particles in contact. Proc.Royal Society. Vol. 269t London, 500–527.

    Google Scholar 

  • Spitzig WA, Sober RJ and Richmond O (1975) Pressure dependence of yielding and associated volume expansion in tempered martensite. Acta Met. 23, 885–893.

    Article  Google Scholar 

  • Spitzig WA, Sober RJ and Richmond O (1976) The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory. Metall. Trans. 7A, 1703–1710.

    Google Scholar 

  • Spitzig WA (1979) Effect of hydrostatic pressure on plastic flow properties of iron single crystals. Acta Met. 27, 523–534.

    Article  Google Scholar 

  • Spitzig WA and Richmond O (1979) Effect of hydrostatic pressure on the deformation behavior of polyethylene and polycarbonate in tension and compresion. Polymer Engng. 19, 1129–1139.

    Article  Google Scholar 

  • Shibata T and Karube D (1965) Influence of the variation of the intermediate principal stress on the mechanical properties of normally consolidated clays. Proc. Sixth Int. Conf. on Soil Mechanics and Found Engrg. Vol. 1. pp 359–363.

    Google Scholar 

  • Sutherland HB and Mesdary MS (1969) The influence of the intermediate principal stress on the strength of sand. Proc. of 7th Int. Conf. on Soil Mechanics and Foundation Engineering, Vol. 1. Mexico City, pp 391–399.

    Google Scholar 

  • Yu Mao-Hong (1961) General behaviour of isotropic yield function (in Chinese), Res. Report of Xi’an Jiaotong University.Xi’an.

    Google Scholar 

  • Yu Mao-Hong (1961) Plastic potential and flow rules associated singular yield criterion (in Chinese), Res. Report of Xi’an Jiaotong University.Xi’an.

    Google Scholar 

  • Yu Mao-Hong (1983) Twin shear stress yield criterion. Int. J. Mech. Sci. 25(1) 71–74.

    Article  Google Scholar 

  • Yu Mao-Hong, He Li-nan and Song Ling-yu (1985) Twin shear stress theory and its generalization, Scientia Sinica (Sciences in China), English Edition, Series A, 28(11), 1174–1183.

    Google Scholar 

Download references

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(2006). Basic Characteristics of Yield of Materials under Complex Stress. In: Generalized Plasticity. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-30433-9_3

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  • DOI: https://doi.org/10.1007/3-540-30433-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25127-9

  • Online ISBN: 978-3-540-30433-3

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