Sommario
Le condizioni di plastificazione che si conoscono presuppongono omogeneità eisotropia del materiale. Per corpi anisotropi sono state proposte espressioni che non possono essere applicate in casi riguardanti le pratiche applicazioni. La condizione di plastificazione proposta dall'A. per i corpi isotropi può essere con opportune trasformazioni adattata a materiali presentanti differenti proprietà meccaniche nelle tre direzioni principali: le formule che se ne ottengono confermano i casi particolari e le formule già note per i corpi isotropi. Le soluzioni proposte dall'A. per i corpi anisotropi sono rappresentate in genere da paraboloidi le cui caratteristiche dipendono ovviamente dai parametri sperimentali.
Summary
The known Limiting Conditions of Yielding presuppose homogeneity andisotropy of the material. Formulas for anisotropic materials have been proposed: but they cannot be applied to all practical applications. The Limiting Condition of Yielding already proposed by the A. for isotropic materials can easily be extended to materials with different mechanical properties in different directions: the formulas obtained confirm the particular cases and the particular formulas already known for isotropic materials. The various solutions proposed by the A. for anisotropic bodies are usually represented by paraboloids whose characteristics obviously depend on the experimental parameters.
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Abbreviations
- σ 1,σ 2,σ 3 :
-
principal normal stresses
- σ 01,σ 02,σ 03 :
-
limit stresses in pure tension along the three principal directions (positive)
- σ 0 :
-
limit stress in pure tension
- σ′01,σ′02,σ′03 :
-
limit stresses in pure compression along the three principal directions (positive)
- σ′0 :
-
limit stress in pure compression
- x=σ 1/σ 01,y=σ 2/σ 02,z=σ 3/σ 03 :
-
non dimensional ratios between the principal normal stresses and the corresponding limit stresses in pure tension
- σ x ,σ y ,σ z :
-
normal non principal stresses
- τ xy ,τ yz ,τ zx :
-
shearing stresses
- τ 0 :
-
limit shearing stress
- δ 1=σ′01/σ 01;δ 2=σ'02/σ 02;δ 3=σ'03/σ 03 :
-
ratios between the limit stresses in pure compression and the corresponding limit stresses in pure tension (positive)
- m=σ 02/σ 01;n=σ 03/σ 01 :
-
ratios of the second and the third limit stress in pure tensionvs. The first limit stress
- m′=σ′02/σ′01;n′=σ′03/σ′01 :
-
ratios of the second and the third limit stress in pure compression vs. the first limit stress
- σ i :
-
hydrostatic limit stress.
References
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F. Stassi,Sui criteri di resistenza dei corpi anisotropi, Atti dell'Accademia di Scienze Lettere e Arti, Palermo. Seduta del 28 Giugno 1968.
F. Stassi,Flow and fracture of materials according to a new limiting condition of yielding, Meccanica, Vol. 2, no. 3, 1967.
L. Rendulic,Eine Betrachtung zur Frage der plastischen Grenzzustande, Der Bauingenieur, 1938.
F. Stassi,Une fonction quadratique des tensions principales comme condition de plasticité des corps solides, Bulletin RILEM, no. 13, Décembre 1961.
F. Stassi,Interdépendance des caractéristiques de résistance des materiaux, Bulletin RILEM, no. 21, Décembre 1963.
F. Stassi,Ancora sui criteri di resistenza dei corpi anisotropi, Atti dell'Accademia di Scienze Lettere e Arti, Palermo, Seduta del 30 Novembre 1968.
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Stassi-D'Alia, F. Limiting conditions of yielding for anisotropic materials. Meccanica 4, 349–363 (1969). https://doi.org/10.1007/BF02133100
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DOI: https://doi.org/10.1007/BF02133100