Size effects associated with skew symmetric Burgers tensor
A. S. Borokinni, O. O. Fadodun, O. P. Layeni, A. P. Akinola, and B. A. Olokuntoye
Available online 06 May 2020

Abstract
This paper investigates size effect phenomena associated with the divergence of the transpose of plastic distortion in plastically deformed isotropic materials. The principle of virtual power, balance of energy, second law of thermodynamics, and codirectionality hypothesis are used to formulate the governing microforce balance and thermodynamically consistent constitutive relations for dissipative microscopic stresses associated with the plastic distortion and skew part of the Burgers tensor. It is obtained that the defect energy through the strictly skew Burgers tensor is converted to the defect energy via the divergence of the plastic distortion. The presence of material length scales in the obtained flow rule indicates that it is possible to apprehend size effects associated with the skew part of the Burgers tensor during the inhomogeneous plastic flow of solid material. Finally and amongst other things, it is shown that the dependency of the microscopic stress vector on the divergence of plastic distortion rate leads to weakening and strengthening effects in the flow rule.

Mathematics Subject Classification
74C10

Keywords
Burgers tensor, flow rule, plastic distortion, polycrystalline, size effects

DOI
https://doi.org/10.2298/TAM191125001B

Investigation of the combined effect of notch and fretting on bending fatigue
Quazi Md. Zobaer Shah, Md. Arefin Kowser, and Mohammad Asaduzzaman Chowdhury
Available online 19 May 2020

Abstract
Being a common phenomenon in failure mechanism, fretting fatigue has emerged as one of the major concerns in recent years both in research and industrial applications. In the present study, the effect of notch and fretting on bending fatigue has been examined by FEM analysis. Based on the available and validated FEM model, analyses have been carried out on single point fretting with a double notch and double point fretting with a single notch respectively. Along the predefined paths through the edge, thickness and notch, fatigue behavior and stress-strain distribution have been studied. It has been found that stress and strain distribution is uniformly spaced for constant fretting loads with a variable concentric load whereas variable fretting loads yield almost two times results. Stress and strain singularity is found for transverse loading when highly stressed. Peak stress was found on the stress distribution path for fretting action for the combined fretting and notch presence. Fatigue life was influenced more drastically by variable fretting loads than variable concentric loadings only in case of tension. Dual action of fretting with notches was found more detrimental than the single action of double fretting/notching.

Mathematics Subject Classification
65-XX; 74-XX

Keywords
contact slip regime, fretting fatigue life, stress-strain distribution, bending load

DOI
https://doi.org/10.2298/TAM191019002Z

A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials
Milan Cajić, Danilo Karličić, Stepa Paunović, and Sondipon Adhikari
Available online 25 May 2020

Abstract
Research on phononic and acoustic materials and structures emerged in the recent decade as a result of switching from theoretical physics to applications in various engineering fields. Periodicity is the main characteristic of the phononic medium stemming from periodic material phases, geometry or the boundary condition with wave propagation properties analysed through frequency band structure. To obtain these characteristics, the generalized Bloch theorem is usually applied to obtain the dispersion relations of viscously damped resonant metamaterials. Here we develop a novel analytical approach to analyse the fractionally damped model of phononic crystals and acoustic metamaterials introduced through the fractional-order Kelvin-Voigt and Maxwell damping models. In the numerical study, the results obtained using the proposed models are compared against the elastic cases of the phononic crystal and locally resonant acoustic metamaterial, where significant differences in dispersion curves are identified. We show that the fractional-order Maxwell model is more suitable for describing the dissipation effect throughout the spectrum due to the possibility of fitting both, the order of fractional derivative and the damping parameter.

Mathematics Subject Classification
34A08; 15A18

Keywords
phononic crystals, acoustic metamaterials, dissipation, fractional viscoelasticity, dispersion relations

DOI
https://doi.org/10.2298/TAM200117003C

An overview of application of micromechanical models in ductile fracture analysis of welded joints
M. Rakin, B. Medjo, N. Gubeljak, and A. Sedmak
Available online 04 June 2020

Abstract
Fracture of welded joints has been an important research and industrial topic for a long time, having in mind the key role of welded joints in ensuring the safe operation and integrity of welded structures. This work contains an overview of application of micromechanical models to ductile fracture of welded joints. The main benefit of these models, in comparison with the classical fracture mechanics approach, is consideration of the local quantities (stress and strain) in prediction of damage development. The damage is quantified through the value of the damage parameter, which is typically related to the void nucleation, growth and coalescence for ductile fracture of metallic materials, i.e. the description of the material can be related to the actual material behaviour during fracture. Most of the presented studies, including those published by the present authors, are performed on steel as the base material, and the rest deal with aluminium alloys.

Mathematics Subject Classification
74R20

Keywords
micromechanical models, welded joint, fracture initiation and development, mismatch

DOI
https://doi.org/10.2298/TAM200117004R