An experimental analysis was undertaken to establish the failure strengths in tension and compression along the strong direction (machine direction) and the weak transverse plane of isotropy (cross direction) for a typical paperboard. The principal strengths of the material along the strong machine direction and on the transverse plane which may be assumed to be approximately isotropic allowed the possibility of forming the elliptic paraboloid failure locus corresponding to this type of material. It was shown that papers in general are tension strong materials having the infinite part of their parabo loid failure surface turned toward the tension-tension-tension octant in the principal stress space.
Get full access to this article
View all access options for this article.
References
1.
Theocans, P.S. "Mechanical and Fracture Characteristics of Paper-Sheets:' Composite Systems for Natural and Synthetic Polymers, Mat Sc1 Monographs No 36, L Salmen, A de Ruvo, J Seferis and E. B Stark , eds Amsterdam Elsevier Publ., pp 173-187 (1986)
2.
Lekhnitskii, S.G.Theory of Elasticity of an Anisotropic Elastic Body. P. Fern, ed , J. J Brandstatter, transl., San FranciscoHolden-Day Inc. ( 1963)
3.
Lekhnitskii, S.G.Anisotropic Plates S. W Tsai and T Cheron, trans. , New YorkGordon and Breach Sci. Publ. ( 1968).
4.
Hill, R. "A Theory of the Yielding and Plastic Flow of Amsotropic Metals," Proc. Roy. Soc. Lond. , Ser. A, Vol. 193, pp. 281-297 (1984)
5.
Hoffman, O. "The Brittle Strength of Orthotropic Materials," Jnl. Comp. Mat. , 1200-206 (1967).
6.
Tsai, S.W. and E.M. Wu. 'A General Theory of Strength for Anisotropic Materials ," Jnl. Composite Mat., 5:58-80 (1971).
7.
Theocaris, P.S. "Failure Criteria for Engineering Materials Based on Anisotropic Hardening," Proc. Nat. Acad. Athens, Ser. A., Vol. 61, pp. 84-114 (1986)
8.
Theocaris, P.S. "Generalized Failure Criteria in the Principal Stress Space," Theoret and Appl. Mech., Bulgarian Academy of Sciences, 19(2):74-104 (1987)
9.
Theocans, P.S. "Failure Characterization of Anisotropic Materials by Means of the Elliptic Paraboloid Failure Criterion," Uspechi Mechanikii (Advances of Mechanics), 10(3) 83-102 (1987).
10.
Tschoegl, N.W. "Failure Surfaces in Principal Stress Space;' in Molecular Order-Molecular Motion : Their Response to Macroscopic Stresses , Jnl. Poly. Sci., Part C, Polymer Symposia, Vol 32. H. H. Kausch, ed. New York:Interscience, pp. 239-267 (1971)
11.
Theocaris, P.S. and Th. Philippidis. "The Paraboloid Failure Surface of Initially Anisotropic Elastic Solids," Jnl. Reinf. Plast and Comp , 6(4) 378-395 (1987).
12.
Theocaris, P.S. "The Elliptic Paraboloid Failure Surface for 2D-Transtropic Plates (Fiber Laminates),"Engng. Fract. Mech. (1988)
13.
Theocaris, P.S. "Failure Criteria for Transtropic, Pressure Dependent, Matenals The Fiber Composites," Rheologica Acta , 27(5):451-465 (1988).
14.
Hill, R. "Theoretical Plasticity of Textured Aggregates," Math. Proc. Cambridge Phil Soc , 85179-192 (1979)
15.
Goldenblatt, I.I. and V.A. Kopnov. "Strength of Glass Reinforced Plastics in the Complex Stress State," Mekhanika Polymerov , 1(2).70-78 (1965)
16.
Coulomb, C.A. "Essai sur l'application des régles des maximis et minimis à quelques problemes de statique relatifs a l'architecture," Mémoires de Mathematiques et de Physique, Acad. Roy des Sciences par divers savants, Vol 7, pp 343-382 (1773)
17.
Norris, C.B. "Strength of Orthotropic Materials Subjected to Combined Stress," Rep No 1816, U.S. Dept of Agriculture, Forest Products Laboratory , Madison, WI (1950)
18.
Theocaris, P.S. "The Paraboloid Failure Surface for the General Orthotropic Material," Acta Mechanica (submitted for publication, 1988).
19.
Suhling, J.C. , R.E. Rowlands, M.W. Johnson and D.E. Gunderson "Tensorial Strength Analysis of Paperboard ," Exper. Mechanics, 25(3):75-84 (1985)
