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The buckling instability of micro- and nanopillars can be an issue when designing intelligent miniaturized devices and characterizing composite materials reinforced with small-scale beam-like particles. Analytical modeling of the buckling of miniaturized pillars is especially important due to the difficulties in conducting experiments. Here, a well-posed stress-driven nonlocal model is developed, which allows the calculation of the critical loads and buckling configurations of the miniaturized pillars on an elastic foundation and with arbitrary numbers of edge cracks. The discontinuities in bending slopes and deflection at the damaged cross-sections due to the edge cracks are captured through the incorporation of both rotational and translational springs. A comprehensive analysis is conducted to investigate the instability of pillars containing a range of one to four cracks. This analysis reveals interesting effects regarding the influence of crack location, nonlocality, and elastic foundation on the initial and subsequent critical loads and associated buckling configurations. The main findings are: (i) the shielding and amplification effects related to a system of cracks become more significant as the dimensions of pillars reduce, (ii) the influence of the shear force at the damaged cross-section related to the translational spring must not be neglected when dealing with higher modes of buckling and long cracks, (iii) an elastic foundation decreases the effects of the cracks and size dependency on the buckling loads, and (iv) the effects of the edge cracks on the critical loads and buckling configurations of the miniaturized pillars are highly dependent on the boundary conditions. [ABSTRACT FROM AUTHOR]

The available experimental results in the literature on the quasi-static bending and free flexural vibration of microcantilevers and nanocantilevers are used to calibrate the length scale parameter of the stress-driven nonlocal elasticity model. The Bernoulli–Euler theory is used to define the kinematic field. The closed form solution derived for the bending problem is used to calibrate the length scale parameter by fitting the load–displacement curves to the experimental results. For the vibration problem, the calibration is done using the least-squares curve fitting method for the natural frequencies. The stress-driven nonlocal theory can adequately capture the size-dependent experimental results. [ABSTRACT FROM AUTHOR]

Mode I fracture behavior of edge- and centrally-cracked nanobeams is analyzed by employing both stress-driven non-local theory of elasticity and Bernoulli–Euler beam theory. The present formulation implements the size-dependency experimentally observed at material micro- and nano-scale, by assuming a non-local constitutive law, that relates the strain to the stress in each material point of the body, through an integral convolution and a kernel. It is observed that the energy release rate decreases by increasing the nonlocality, showing the superior fracture performance of nanobeams with respect to large-scale beams. [ABSTRACT FROM AUTHOR]

A novel approach is proposed to determine a physically meaningful length-scale parameter for the phase-field modeling of macroscale fracture in metal–ceramic composites on an example of chromium–alumina composite fabricated by powder metallurgy. The approach is based on the fractography analysis by the scanning electron microscopy (SEM) with the aim to measure the process zone size and use that value as the length-scale parameter in the phase-field modeling. Mode I and mixed-mode I/II fracture tests are conducted on Cr–Al2O3 composites at different reinforcement volume fractions and particle sizes using single-edge notched beams under four-point bending. The fracture surfaces are analyzed in detail by SEM to determine the size of the process zone where the microscale nonlinear fracture events occur. The model adequately approximates the experimentally measured fracture toughness and the fracture loads. It is shown that the model prediction of the crack initiation direction under the mixed-mode loading is in agreement with the experiments and the generalized maximum tangential stress criterion. These outcomes justify using the process zone size as the scale parameter in the phase-field modeling of macroscale fracture in chromium–alumina and similar metal–ceramic composites. [ABSTRACT FROM AUTHOR]

A novel mathematical formulation is presented for the applications of the stress-driven nonlocal theory of elasticity to engineering nano-scale problems requiring longitudinal discretization. Specifically, a differential formulation accompanied with novel constitutive continuity conditions is provided for determining exact closed-form solutions of nonlocal Euler-Bernoulli beams with loading discontinuities, i.e. points of discontinuity for external loads and internal forces. Constitutive continuity conditions have to be satisfied in interior points where a loading discontinuity occurs and contain integral convolutions of the stress over suitable parts of the nonlocal beam. Several results show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The instability of nanobeams rested on two-parameter elastic foundations is studied through the Bernoulli–Euler beam theory and the stress-driven nonlocal elasticity model. The size-dependency is incorporated into the formulation by defining the strain at each point as an integral convolution in terms of the stresses in all the points and a kernel. The nonlocal elasticity problem in a bounded domain is well-posed and inconsistencies within the Eringen nonlocal theory are overcome. Excellent agreement is found with the results in the literature, and new insightful results are presented for the buckling loads of nanobeams rested on the Winkler and Pasternak foundations. [ABSTRACT FROM AUTHOR]

In this paper, finite element method is implemented to model stranded-wire helical springs under different loading conditions. Finite element results are coupled with multiaxial fatigue criteria such as Fatemi–Socie and Kandil–Brown–Miller together with a uniaxial fatigue criterion, Coffin–Manson, to predict fatigue life of the stranded-wire helical springs. It is shown that due to damping effects between wires, stranded-wire helical springs have longer fatigue life compared to their equivalent single-wire helical springs at a similar condition. It is also demonstrated that fatigue life is longer for loadings with higher initial displacement of spring head. As practical examples, fatigue life of stranded-wire helical springs with 9 and 15 wires are estimated and compared. It is shown that the spring with 15 wires gives longer fatigue life. It is also observed that Kandil–Brown–Miller and Fatemi–Socie criteria give the least and the highest fatigue life prediction, respectively. [ABSTRACT FROM AUTHOR]