Fracture criteria under creep with strain history taken into account,and long-term strength modelling |
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Authors: | A V Khokhlov |
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Institution: | 1.Institute of Mechanics,Lomonosov Moscow State University,Moscow,Russia |
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Abstract: | In the present paper, we continue to study the nonlinear constitutive relation (CR) between the stress and strain proposed
in 1] to describe one-dimensional isothermal rheological processes in the case of monotone variation of the strain (in particular,
relaxation, creep, plasticity, and superplasticity).
We show that this CR together with the strain fracture criterion (FC) leads to theoretical long-term strength curves (LSC)
with the same qualitative properties as the typical experimental LSC of viscoelastoplastic materials. We propose two parametric
families of fracture criteria in the case of monotone uniaxial strain, which are related to the strain fracture criterion
(SFC) but take into account the strain increase history and the dependence of the critical strain on the stress. Instead of
the current strain, they use other measures of damage related to the strain history by time-dependent integral operators.
For any values of the material parameters, analytic studies of these criteria allowed us to find several useful properties,
which confirm that they can be used to describe the creep fracture of different materials. In particular, we prove that, together
with the proposed constitutive relations, these FC lead to theoretical long-term strength curves (TLSC) with the same qualitative
properties as the experimental LSC. It is important that each of the constructed families of FC forms a monotone and continuous
scale of criteria (monotonously and continuously depending on a real parameter) that contains the SFC as the limit case. Moreover,
the criteria in the first family always provide the fracture time greater than that given by the SFC, the criteria in the
second family always provide a smaller fracture time, and the difference can be made arbitrarily small by choosing the values
of the control parameter near the scale end. This property is very useful in finding a more accurate adjustment of the model
to the existing experimental data describing the fracture time dependence on the stress, temperature, radiation, and other
factors: if these data are poorly described by the SFC, then one can choose a more appropriate criterion from the constructed
families by varying the value of the control parameter smoothly and monotonously. |
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