Closure to “Discussions of ‘Elastic Waves Created During Tensile Fracture: The Phenomenon of a Second Fracture’” (1953, ASME J. Appl. Mech., 20, pp. 583–585)

Abstract In some tensile tests with brittle materials, it was noted that fractures were produced at two different cross sections of the specimen when the rupture load was reached. The phenomenon of the second fracture prompted the present investigation. It is believed that the second fracture is caused by the destructive action of the elastic strain waves created during the first of the two fractures. The analytical and experimental work carried out was focused on describing the character of these waves. Consideration of the mechanics involved reduces the problem to that of a vibrating cantilever beam with time-dependent boundary conditions. Two types of waves are shown to exist. The first is a longitudinal unloading wave (compression). The other is a group of flexural strain waves caused by the moment that develops at the initial fracture section. The methods of operational mathematics and the electric-analog computer have been employed in the analytical study.

Download Full-text

Remarks on nonlinear elastic waves with null conditions

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2020039 ◽

2020 ◽

Vol 26 ◽

pp. 121

Author(s):

Dongbing Zha ◽

Weimin Peng

Keyword(s):

Initial Data ◽

Global Existence ◽

Elastic Waves ◽

Wave Equations ◽

Alternative Proof ◽

Classical Solutions ◽

Small Initial Data ◽

Hyperelastic Materials ◽

Variational Structure ◽

Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

Download Full-text

THEORY OF THE ATTENUATION OF ELASTIC WAVES IN INHOMOGENEOUS SOLIDS

Le Journal de Physique Colloques ◽

10.1051/jphyscol:1981632 ◽

1981 ◽

Vol 42 (C6) ◽

pp. C6-102-C6-104

Author(s):

P. G. Klemens

Keyword(s):

Elastic Waves

Download Full-text

Microstructural and Mechanical Behaviour Evaluation of Mg-Al-Zn Alloy Friction Stir Welded Joint

International Journal of Automotive and Mechanical Engineering ◽

10.15282/ijame.17.3.2020.08.0612 ◽

2020 ◽

Vol 17 (3) ◽

pp. 8150-8159

Author(s):

Kulwant Singh ◽

Gurbhinder Singh ◽

Harmeet Singh

Keyword(s):

Heat Treatment ◽

Friction Stir Welding ◽

Magnesium Alloys ◽

Mechanical Performance ◽

Fuel Efficiency ◽

Research Work ◽

Grain Structure ◽

Tensile Fracture ◽

Friction Stir ◽

The Impact

The weight reduction concept is most effective to reduce the emissions of greenhouse gases from vehicles, which also improves fuel efficiency. Amongst lightweight materials, magnesium alloys are attractive to the automotive sector as a structural material. Welding feasibility of magnesium alloys acts as an influential role in its usage for lightweight prospects. Friction stir welding (FSW) is an appropriate technique as compared to other welding techniques to join magnesium alloys. Field of friction stir welding is emerging in the current scenario. The friction stir welding technique has been selected to weld AZ91 magnesium alloys in the current research work. The microstructure and mechanical characteristics of the produced FSW butt joints have been investigated. Further, the influence of post welding heat treatment (at 260 °C for 1 h) on these properties has also been examined. Post welding heat treatment (PWHT) resulted in the improvement of the grain structure of weld zones which affected the mechanical performance of the joints. After heat treatment, the tensile strength and elongation of the joint increased by 12.6 % and 31.9 % respectively. It is proven that after PWHT, the microhardness of the stir zone reduced and a comparatively smoothened microhardness profile of the FSW joint obtained. No considerable variation in the location of the tensile fracture was witnessed after PWHT. The results show that the impact toughness of the weld joints further decreases after post welding heat treatment.

Download Full-text