Abstract
Inelastic behavior of thick-walled cylinders subjected to nonproportionate loading was studied by the testing of specimens made of C1045 steel and of annealed copper. Several theories were reviewed. A closed-form solution proposed by Mendelson12 was used to predict external strains for open-end and closed-end thick-walled cylinders. An incremental theory proposed by Chu13 was used to provide incremental solutions for open-end thick-walled cylinders, and for cylinders subjected to nonproportionate loading.
Test data for open-end and closed-end thick-walled cylinders made of C1045 steel and of annealed copper were in excellent agreement with the incremental theory. Larger values were predicted by use of the closed-form solution for circumferential strains than actual test data for open-end thick-walled cylinders at large depth of yielding. For cylinders subjected to nonproportionate loading, excellent agreement was indicated between the incremental theory and the experiments for the plot of axial load vs. circumferential strain for specimens made of both metals. Agreement between the incremental theory prediction of axial strains for the specimens made of annealed copper and test data is quite satisfactory. Larger values were predicted by the incremental theory for axial strain than experimental data for specimens made of C1045 steel. The error was conservative.
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Abbreviations
- \(\sigma _o , \varepsilon _o = \sigma _o /E\) :
-
initial yielding stress and initial yielding strain in tension, respectively
- \(\sigma , \sigma = \frac{\sigma }{{\sigma _o }}\) :
-
normal stress and dimensionless normal stress, respectively
- \(\sigma _r , \sigma _\theta , \sigma _z\) :
-
principal stresses
- \(\varepsilon , \varepsilon = \varepsilon /\varepsilon _o\) :
-
normal strain and dimensionless normal strain, respectively
- \(\varepsilon _r , \varepsilon _\theta , \varepsilon _z\) :
-
principal strains
- \(\varepsilon ', \varepsilon ''\) :
-
elastic and inelastic normal strain, respectively
- \(\bar \sigma\) :
-
effective stress defined in eq (7)
- \(\bar \varepsilon ''\) :
-
dimensionless effective plastic strain defined in eq (9)
- \(\bar \sigma = \frac{{\bar \sigma }}{{\sigma _o }}, \bar \varepsilon = \frac{{\bar \varepsilon }}{{\varepsilon _o }}\) :
-
dimensionless effective stress and dimensionless effective strain, respectively
- r,ρ=r/a :
-
radius and dimensionless radius, respectively
- a,b :
-
inside and outside radius of a thick-walled cylinder
- E :
-
Young’s modulus
- μ:
-
Poisson’s ratio
- α:
-
strain-hardening factor for material
- P i ,P o :
-
internal and external pressure, respectively
- \(\sigma _r , \sigma _\theta , \sigma _z\) :
-
dimensionless principal stresses defined in eq (1)
- \(\varepsilon _r , \varepsilon _\theta , \varepsilon _z\) :
-
dimensionless principal strains defined in eq (2)
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Chu, S.C., Vasilakis, J.D. Inelastic behavior of thick-walled cylinders subjected to nonproportionate loading. Experimental Mechanics 13, 113–119 (1973). https://doi.org/10.1007/BF02323968
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DOI: https://doi.org/10.1007/BF02323968