PSI - Issue 32

Yuriy Bayandin et al. / Procedia Structural Integrity 32 (2021) 26–31 Author name / Structural Integrity Procedia 00 (2019) 000–000

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2

Nomenclature σ stress ε strain E

Young's modulus

continuity parameter (structural-scaling parameter)

δ

damage parameter intensity of defects kinetic coefficient

ω p Γ

stress amplitude of cyclic loading cycle asymmetry coefficient

σ A

R

loading frequency

ν

number of loading cycles

N

ultimate stress

σ B σ c

fatigue limit stress Numerical simulation of deformation and failure of structural elements made of composite materials requires constitutive equations and mathematical models development, capable of adequately describing the behavior of composite material with regard to external factors − loading rate, temperature, type of stress-strain state and other factors, including structural changes caused by the accumulation of damage under cyclic loading, Arutyunyan and Arutyunyan (2010), Arutyunyan (2019). Phenomenological constitutive equations, the type and parameters of which are established by the results of quasi-static, including cyclic, and dynamic tests of composite materials (standard types of tensile/compression, bend, shear tests, etc.) are widely used. Identification of constitutive equations and mathematical models on their basis should be used in numerical simulation to predict the behavior of the real structure if the developed models are verified after that process. Usually, verification is carried out by comparison of experimental results of standard tests of a specimen and its numerical (finite-element) analogue using the identified parameters of the model of deformation and failure of composite materials. The development of deformation and fracture models for composite materials under cyclic loading that take into account damage accumulation during deformation and influence on physical and mechanical characteristics is of current interest. Traditionally, studies of high cycle fatigue have been performed on structural metals and alloys, Murakami (2019). The material fatigue failure process is defined as the gradual accumulation of damage in the material as a result of alternating, cyclic repeated loads. This process is cumulative and irreversible, and leads to the degradation of mechanical properties of materials, emergence and accumulation of damage with further initiation of micro- and macrocracks, Kachanov (2013). The high cycle fatigue of materials is defined by a number of loading cycles greater than 10 5 . In this case, at each cycle of loading it is assumed that the sample is deformed elastically on the macroscale, despite this high cycle fatigue is characterized by the emergence of irreversible processes at the meso- and microscales. The basic patterns of fatigue failure can be seen in the fatigue curve proposed by Wöhler (1870). It shows the relationship between stress/strain amplitudes and the number of cycles before macroscopic failure. The purpose of this work is to describe the fatigue curve, including modeling the degradation of the effective elastic modulus due to damage accumulation in a composite material. 2. Theory of damage accumulation in material According to effective elastic properties representation proposed by Kachanov (1992) and the model developed by Bayandin et al. (2016), the effective stress in a composite material, taking into account the damage, can be written in the following form (in the uniaxial loading):

(1)

eff eff E E σ = ε = δε ,

3 − structural scaling parameter, characterizing the value of

where E is Young's modulus, ε is strain, δ = ( r / r 0 )