PSI - Issue 42

D. Kosov et al. / Procedia Structural Integrity 42 (2022) 545–552 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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various profiles. In this regard, it is relevant to determine the limiting state of such structures in a complex stress state under conditions of stress concentration. The description of material properties under conditions of monotonic static deformation took place in classical and modern strength theories proposed by Novozhilov et al. (1969), Lomakin et al. (1978, 1988, 2011), Pisarenko et al. (1976). Experimental determination of limit stresses is a very costly task from a practical point of view, so the formulation of theories of the limit state by Shlyannikov (2014) is of great importance. Limit state theories contain parameters or functions that are sensitive to the type of stress state according to Potapova (2005), Makhutov (2008).

Nomenclature ω

damage parameter specimen thickness energy release rate Poisson`s ratio hydrostatic stress

Young`s modulus

E

yield stress

t

σ 0

asymptotic limit of temporary resistance

strain hardening exponent

R inf

γ , n r, s

constant material triaxial function shear modulus

Y ν p

R v G

In the engineering, understanding the mechanisms of damage to solids is critical to the safe operation of structural elements. Damage at the microscopic level in the form of micropores and cracks can lead to a loss in the bearing capacity of the material. To accurately predict such mechanisms at the product design stage, appropriate damage models are required. The use of such models in the finite element method can be a useful tool for the design and operation of structural elements. In the model used, the combination of the law of isotropic hardening and the law of damage accumulation Lemaitre by Neto, Peric (2008) is implemented. In this times, a number of models are known, which can be divided into models based on micromechanics and phenomenological models. A detailed literature review on damage models can be found in Azinpour (2018). One of the micromechanical formulations was developed by Rice and Tracey (1969), which focused attention on the microscopic development of a spherical void in a rigid ideally plastic material matrix. The formulation developed by Rice and Tracey was further developed by Gurson (1977) and Tvergaard, Needleman (1984), who present internal degradation as a volume fraction of voids (porosity). The first model based on the continuum fracture mechanics approach was proposed by Kachanov (1958). He introduced a scalar internal variable to model creep failure of metals under uniaxial loads. The physical value of the damage variable was given later by Rabotnov (1963), who proposed to consider the reduction in the cross-sectional area due to microcracks as a measure of the state of internal damage. Over time, the concept of internal damage variable has been generalized by a number of the authors to three dimensional situations. For example, Leckie and Hayhurst (1974) used the idea of effective bearing area reduction as a scalar measure of material wear to determine the creep model under multiaxial stresses. The scalar damage variable was also considered by Lemaitre and Chaboshe et.al. (1988,1985) in defining a purely phenomenological model of plastic isotropic damage in metals. Based on the strain equivalence hypothesis, which states that the deformation behavior of a damaged material is represented by the constitutive laws of an undamaged material with the true stress replaced by the effective stress. This law is postulated in which the standard definition of the damage parameter in terms of reduction of the bearing surface is replaced in the Lemaitre model by a decrease in the modulus of elasticity in ideally isotropic case. Damage in the material at the microlevel affects the nature of its fracture, therefore, to solve the problem of estimating the safety strength of the material, it is necessary to use a damage accumulation model. The purpose of this study is to determine the impact of accumulated damage in a material that is under a complex stress state, on the characteristics of their bearing capacity. One of the purpose of this work is the presentation of a limit state diagram based on the true values of stresses and strains, taking into account the damage of the material.