Quantized fracture mechanics

A new energy-based theory, quantized fracture mechanics (QFM), is presented that modifies continuum-based fracture mechanics; stress- and strain-based QFM analogs are also proposed. The differentials in Griffith's criterion are substituted with finite differences; the implications are remarkable. Fracture of tiny systems with a given geometry and type of loading occurs at ‘quantized’ stresses that are well predicted by QFM: strengths predicted by QFM are compared with experimental results on carbon nanotubes, β-SiC nanorods, α-Si₃N₄ whiskers, and polysilicon thin films; and also with molecular mechanics/dynamics simulation of fracture of carbon nanotubes and graphene with cracks and holes, and statistical mechanics-based simulations on fracture of two-dimensional spring networks. QFM is self-consistent, agreeing to first-order with linear elastic fracture mechanics (LEFM), and to second-order with non-linear fracture mechanics (NLFM). For vanishing crack length QFM predicts a finite ideal strength in agreement with Orowan's prediction. In contrast to LEFM, QFM has no restrictions on treating defect size and shape. The different fracture Modes (opening I, sliding II and tearing III), and the stability of the fracture propagations, are treated in a simple way.     

Autowave mechanics of plastic flow in solids

The regularities of the development of localized plastic deformation of solids have been analyzed. A correlation of the products of linear and velocity parameters of elastic and plastic deformations is found for some metals and nonmetals. A hypothesis about relationship between the characteristics of elastic and plastic deformation is formulated on this basis. An empirical relationship between the regularities of plastic flow and quantum-mechanical characteristics is found.     

The fracture mechanics of glassy polymers

The application of fracture mechanics to glassy polymers, in particular crack growth in PMMA, is discussed. Particular attention is paid to two processes which modulate the energy supply to the crack tip: viscoelastic dissipation at slow crack speeds and specimen inertia at large crack speeds. The relation between fracture energy and crack speed is reviewed, and, where possible, fracture surface observations are correlated with dynamic behavior.     

Energy balance in deformation mechanics of solids at low temperatures

The model of a solid in the form of an ensemble of independent anharmonic oscillators arranged in a uniform stress field has been considered to analyze the energy balance during adiabatic mechanical loading of a solid at low temperatures. Oscillator elongation is determined as the average over the ensemble, and a part of its energy is matched to this quantity. This part has the physical meaning of the mechanical energy of sample deformation and becomes a part of the energy balance upon deformation. After averaging, the uniform force field is replaced by the resultant force associated with the average deformation. Another component of the balance at low temperatures is the energy of zero-point vibrations of oscillators. Thus, upon mechanical deformation of a solid, the energy exchange occurs between two scale levels: the atomic vibration energy at a microlevel and the macroscopic deformation energy of the sample as a whole.     

Microscopic treatment of the fracture process in solids

The process of brittle fracture in a solid is presented as the formation and evolution of an ensemble of elementary carriers (frustrons). The latter represent a mesoscopic region of localized strong shear deformations surrounded by an envelope of an elevated level of plastic flow. The conditions of fluctuation generation of frustrons, their characteristics, and the growth of the supercritical cluster are determined. The fracture time is derived.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 29–35, September, 1987.     

Hybrid method in elastic and elastoplastic fracture mechanics

The utility of the hybrid experimental–numerical method in elastic and elastoplastic fracture mechanics is demonstrated through a fracture process zone analysis and a J-integral computation, respectively. For the former, the crack bridging stresses in the fracture process zones of concrete and alumina fracture specimens were determined through an inverse analysis and the dissipated energies in these zones were quantified. For the latter, J-integral was shown to be highly path dependent with stable crack growth.     

Comparison of time dependent fracture in viscoelastic and ductile solids

Effects of two parameters on enhancement of the time-dependent fracture manifested by a slow stable crack propagation that precedes catastrophic failure in ductile materials have been studied. One of these parameters is related to the material ductility (ρ) and the other describes the geometry (roughness) of crack surface and is measured by the degree of fractality represented by the fractal exponent α, or — equivalently — by the Hausdorff fractal dimension D for a self-similar crack. These studies of early stages of ductile fracture are preceded by a brief summary of modeling the phenomenon of delayed fracture in polymeric materials, sometimes referred to as “creep rupture”. Despite different physical mechanisms involved in the preliminary stable crack extension and despite different mathematical representations, a remarkable similarity of the end results pertaining to the two phenomena of slow crack growth that occur either in viscoelastic or ductile media has been demonstrated.     

Electromagnetic phenomena entailed by deformation and fracture of dielectric solids

Mechanoelectric effects caused by elastic deformation of glasses and marbles are studied in a neutral environment and with weak electric polarization of samples. It is found that the electric potentials that are produced by bending a sample are opposite in sign in compressed and stretched regions. The mechanoelectric effects increase or decrease depending on the direction of the electric field applied to the sample. It is concluded that the electric polarization and the polarization induced by mechanical deformation are of a common nature. Electromagnetic precursors of earthquakes are discussed.     

Scaling of crack surfaces and implications for fracture mechanics

The scaling laws describing the roughness development of crack surfaces are incorporated into the Griffith criterion. We show that, in the case of a Family-Vicsek scaling, the energy balance leads to a purely elastic brittle behavior. On the contrary, it appears that an anomalous scaling reflects an R-curve behavior associated with a size effect of the critical resistance to crack growth in agreement with the fracture process of heterogeneous brittle materials exhibiting a microcracking damage.     

Rigorous field-theoretical approach to the contact mechanics of rough elastic solids

A statistical field theory is formulated, which allows one to calculate the pressure distribution Pr(p) in a contact formed by an elastic body and a rigid counter face of arbitrary topography. It is a cumulant expansion, which contains Persson's contact mechanics theory as the leading-order term. Our approach provides a framework with which corrections can now be derived systematically. As an example, Pr(p) is calculated to high accuracy for exponentially repulsive solids. Non-Gaussian tails in Pr(p) can be rationalized for surfaces whose height spectra differ from colored noise.     

动态断裂力学的无网格流形方法

运用无网格流形方法求解动态断裂力学问题.该方法利用单位分解法和有限覆盖技术建立形函数，形函数的建立不受域内不连续的影响，可较好地求解裂纹问题.对于局部化问题，该方法的形函数构造较其他方法更为有效，避免了其他方法在建立试函数时没有考虑不连续尖端的缺点.由于采用有限覆盖技术建立试函数，该方法克服了不连续对试函数的影响，尤其当不连续变得复杂时，更能显示该方法在处理不连续方面的优点.在求解动态断裂力学问题时，弹性动力学积分弱形式的推导采用加权残数法，空间离散采用基于单位分解法的无网格流形方法，时间离散主要采用Newmark法.最后给出两个数值算例，将计算结果与解析解对比，说明该方法的正确性和可行性. 关键词： 有限覆盖 无网格流形方法 动态断裂力学 动态应力强度因子     

Hybrid numerical methods in static and dynamic fracture mechanics

In this article, the concept of the hybrid numerical methods is clarified. On the basis of this concept, various hybrid numerical methods used in static and dynamic fracture mechanics are classified into five categories: (i) hybrid experimental–numerical methods, (ii) hybrid numerical–experimental methods, (iii) hybrid analytical–numerical methods, (iv) hybrid numerical–analytical methods, and (v) hybrid numerical–numerical methods. Features of each category of hybrid numerical method are presented with pertinent numerical results.     

Finite element mapping for spring network representations of the mechanics of solids

We present a general finite element mapping procedure for defining spring network representations of solid mechanics. The procedure is rigorous and equally suitable for setting regular and unstructured spring network models of generally anisotropic solids. We use the procedure to define close-packed triangular and simple cubic lattice spring models of isotropic 2D and 3D elastic media, respectively. We extend the study to heterogeneous solids and show that the mapped spring network approach constitutes an appealing route for incorporating subelement level constitutive equations.     

Role of local nanostructural states in plastic deformation and fracture of solids

The paper substantiates the concept of physical mesomechanics that the basis for nonlinear behavior of solids under plastic deformation and fracture is the formation of nanostructural states in local highly nonequilibrium zones. Their structural transformations and two-phase decay govern the generation of strain-induced defects and cracks. Nonlinear wave mechanisms of nanostructural states influence on plastic deformation and fracture are discussed.