Effect of anisotropy on the large strain creep behavior of composite thick-walled spherical vessels

Abstract

The steady-state creep behavior of a thick-walled composite spherical vessel is investigated. The vessel is assumed to be undergoing large strains and made of a material with anisotropic properties. The research presented in this work employs a steady-state creep law for composite materials including a threshold stress. The mathematical expressions for the stresses, strains and strain rates in the anisotropic spherical vessel are derived and the results are presented for five cases of anisotropy. In the absence of experimental values, a theoretical method to estimate the anisotropic constants is also included in the paper. Numerical results and graphs are presented to study the effect of anisotropy on the large creep strain behavior of the composite spherical vessel. Based on the results obtained from the present investigations, it can be concluded that the anisotropy of the material can be beneficially utilized for the reduction in the stress, strains, and strain-rates values from the corresponding values for an isotropic material, and, thus, a longer life for the spherical vessel may be achieved.

Appendix A

Bhatnagar and Gupta [12] present the following relations for an anisotropic (orthotropic) material in cylindrical coordinate system $r,\theta ,{\text{and }}z.$

Effective stress defined as

$$ \sigma = \frac{1}{\sqrt 2 }\left[ {F\left( {\sigma_{\theta } - \sigma_{z} } \right)^{2} + G\left( {\sigma_{z} - \sigma_{r} } \right)^{2} + H\left( {\sigma_{r} - \sigma_{z} } \right)^{2} } \right]^{1/2} $$

(28)

is related to effective strain rate $\dot{\varepsilon }$ by the equation

$$ \sigma = f\left( {\dot{\varepsilon }} \right) $$

(29)

The constitutive equations for creep are

$$ \varepsilon_{r} = \frac{\varepsilon }{2\sigma }\left[ {\left( {G + H} \right)\sigma_{r} - H\sigma_{\theta } - G\sigma_{z} } \right] $$

(30)

$$ \varepsilon_{\theta } = \frac{\varepsilon }{2\sigma } \left[ {\left( {H + F} \right)\sigma_{\theta } - F\sigma_{z} - H\sigma_{r} } \right] $$

(31)

$$ \varepsilon_{z} = \frac{\varepsilon }{2\sigma } \left[ {\left( {F + G} \right)\sigma_{z} - G\sigma_{r} - F\sigma_{\theta } } \right] $$

(32)

In the above equations, the subscripts $r, \theta ,\, and\, z$ refer to the radial, tangential, and axial directions, respectively. The strain rates in the three directions can be obtained by differentiating Eqs (30), (31), and (32) with respect to time t.