Dynamic stress control of bi-material structure subjected to sawtooth shock pulse based on interface characteristics
Introduction
Over the years, a large body of work on dynamic stress has accumulated. Most studies are focused on the stress state and its related parameters, which is the basis of strength evaluation. El-Hadek makes a research on the dynamic equivalence of ultrasonic stress wave in solids [1]. Zhang et al. investigate the dynamic compression characteristic of 6005 aluminum alloy aged at elevated temperatures [2]. Jr. et al. analyze the critical stress of commercial pure titanium in the initial stage of dynamic transformation [3]. Qiao et al. make a study on the dynamic stress concentration around a spherical inclusion in a thick spherical shell [4]. Xu et al. unravel the crack propagation mechanism and the brittle dynamic stress intensity factors of PVB laminated glass plates [5]. Mikulich et al. improve the boundary integral equation method to calculate the dynamic couple stress [6]. Myung et al. analyze the dynamic stress of the measurement part of circular contour specimen for ultrasonic fatigue test [7]. Sheikhhassani et al. make a research on the dynamic stress concentration along the interfaces of multiple multilayered inclusions embedded in a half-space excited by a plane harmonic SH-wave [8]. Menshykov et al. investigate the effect of friction of the crack faces on linear crack of homogeneous material under the action of an oblique harmonic loading [9]. Zhao et al. investigate the dynamic stress intensity factors of rail cracks at high speeds by using explicit FEM [10]. Liu et al. study the dynamic stress intensity factors of 3D rectangular cracks in a transversely isotropic elastic material caused by an incident harmonic stress wave by generalizing Almansi's theorem and Schmidt method [11].
The mechanical properties of the bi-material have also been discussed in some studies, since it possesses some unique characters. Figiel et al. propose a probabilistic approach to sensitivity analysis of a fatigue delamination problem of a bi-layer composite [12]. Selvadurai studies the contact mechanics of bi-material elastic solid based on the classic results of R.D. Mindlin [13]. Mamalis et al. investigate the plastic failure of a bi-material tube in the axial direction [14]. Wisessint et al. study the stress singularity in plastic range of a bi-material joint [15]. Belhouari et al. and Farahani et al. focus on the elastic-plastic properties of bi-material structures [16,17]. Yuan et al. make a research on the problem of wrinkling of the liner of a bi-material pipe subjected to axial compression [18]. Coelho et al. and Alberdi et al. focus on the topological optimization of bi-material structures [19,20]. Dundurs et al. study the stress state at the interface of three-dimensional bi-material by using the continuous conditions of plane strain and curvature [21]. Suhir et al. develop an analytical model to evaluate the stress and strain of a bi-material structure with a compliant bonding layer [22]. In addition, some studies also pay great attention on the propagation of elastic waves at the interface of bi-material [23,24].
It is imperative to tackle the issue related to the crack of the bi-materials. Mikucka et al. study the elastodynamic properties of an interface crack of bi-material subjected to an oblique harmonic loading [25]. Furthermore, Yang et al. analyze the dynamic stress intensity factor of the interfacial crack near the shallow circular inclusions in the bi-material half space [26]. Dineva et al. and Chirino et al. conduct a similar research respectively, except that a normal harmonic loading instead of an oblique harmonic loading [27,28] is utilized. The crack at the interface of bi-material resulted from the impact loading respectively is investigated [29,30].
The studies above have significantly theoretical and practical purposes. All shed light on some other mechanical properties rather than another vital one – the stress control of the main structure. However, this study, based on the analytical method and the numerical models, examines both the phenomenon and mechanism of stress control of bi-material structures, which have not been covered and discussed by the existing studies.
Section snippets
Mathematical principles
Elastic waves are generated in a structure, which is excited by a dynamic loading. In general, longitudinal and transverse waves in solids exist simultaneously. Concerning its simplicity, a 2D plane strain problem is considered here.
To simplify the mathematical derivation, it is assumed that the medium is infinite and the elastic waves propagate in the x-direction. Thus, the displacements of particles in both longitudinal and transverse waves may be expressed as functions of x coordinate and
Governing equations
The mechanical behavior of an elastic body is governed by equilibrium equation, strain-displacement equation and constitutive equation. According to the literature [12], these three equations for the interior of composite constituent are respectively expressed asand where, σ denotes the stress tensor, ε denotes the strain tensor, U denotes the displacement vector, C denotes the constitutive matrix, Xn denotes an element of the composite
Average stresses
The time-history curves of average stresses in the three models are shown in Fig. 4. Thus, The findings are that (1) for the bi-material models (WC-AL model and PA-AL model), the wave frequencies of different materials in the same model are consistent; (2) the AL stress of WC-AL model is much less than the WC stress in the same model, while the AL stress of PA-AL model is much greater than the PA stress in the same model; (3) the AL stress of WC-AL model is obviously less than that of AL model,
Conclusions
In this study, the factors that could have an impact on dynamic stress are analyzed analytically, and then the dynamic stresses of two bi-material models and a homogenous material model is studied by numerical method. It suggests that under the action of same sawtooth shock pulse, the ratio of stresses in different materials of the same model mainly depends on the acoustic impedance, the ratio of thickness to width of material and the Poisson's ratio. Furthermore, it demonstrates that the ratio
Declaration of Competing Interest
We declare that we have no conflicts of interest to this work, and have no any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
Acknowledgement
The work is supported by the National Natural Science Foundation of China (Grant No. 51709229) and Natural Science Basic Research Planin Shaanxi Province of China (Grant No. 2018JQ5092).
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Contact problems for cracks under impact loading
2020, Procedia Structural IntegrityImpact Loading of Interface Cracks: Effects of Cracks Closure and Friction
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