It is universally considered that the creep deformation is caused by shears, developing along lines of the main tangential stresses. Constitutive relations are derived by projecting the said shears on the main stress axes and by adding the elastic strains. The material failure is initiated when the maximum shear reaches a critical value and causes the loss of the shear strength. This approach makes the grounds to take into account the material failure under creep conditions without using the Kachanov-Rabotnov kinetic damage equation. The model, based on the maximum tangential stress and the exponential law is used to solve the problem of deformation and failure of an elastic-creep body at the unsteady and steady creep stages. The cylindrical and spherical cavities in an infinite body are considered under the internal and external pressures. Stresses, creep strains, time of the failure initiation, a failure-front location and the velocity of failure front propagation are evaluated at every instant of time.
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