Formulation of the material force approach for elastic and inelastic materials

Fracture mechanical investigations are important for the durability of fracture sensitive products. Fracture mechanical simulations help to shorten the product development cycle and to decrease product costs. The so-called material force approach as an efficient tool is used to determine fracture mechanical parameters for elastic and inelastic materials. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

平面应力状态断裂强度的椭圆准则分析

简要分析了近年来提出的一个断裂准则——椭圆准则的基本特征,导出了它在主应力坐标系下的基本方程.根据所导出的基本方程,获得了平面应力条件下椭圆准则理论断裂强度曲线的完整描述关系,并分析讨论了破坏发生的方位及断裂形式与材料本征力学性质参数之间的联系.与既有理论结果及实验现象的对比解释了椭圆准则在材料相关参数确定方面的局限性.当应力状态相关材料特征参数在拉伸区和压缩区均作为常数时,获得了铸铁和混凝土平面应力状态下的断裂强度曲线.与相关实验数据的对比表明,它们在拉伸区能较好地吻合,但压缩区的差异十分显著,进一步证实了材料特征参数随应力状态变化规律对椭圆准则发展的必要性.     

Fracture Mechanical Analysis of Cracks in Ice Shelves using the Finite Element Method and Configurational Forces

Ice shelves are important elements of the climate system and sensitive to climate changes. The disintegration of large Antarctic ice shelves is the focus of this fracture mechanical analysis. Ice is a complex material which, depending on the context, can be seen as a viscous fluid or as an elastic solid. A fracture event usually occurs on a rather short time scale, thus the elastic response is important and linear elastic fracture mechanics can be used. The investigation of the stress intensity factor as a measure of crack tip loading is based on a 2-dimensional analysis of a single crack with a mode-I type load and additional body loads. This investigation is performed using configurational forces. Depth dependent density and temperature profiles are considered. The relevant parameters are obtained by literature, remote sensing data analysis and modeling of the ice dynamics. The criticality of wet surface cracks is investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A combined molecular dynamics-phase-field modelling approach to fracture

In order to better understand and ease the determination of material and model parameters required for the macroscopic modelling of brittle fracture, a bottom-up comparative study between molecular dynamics (MD) simulations and the continuum phase-field modelling (PFM) is carried out. In particular, based on the MD simulations of fracture of a highly brittle material, a number of PFM parameters such as the width of the transition zone between the damaged and the undamaged material, the crack resistance and the elasticity modulus are estimated. This study opens the door for an efficient way for multi-scale modelling of fracture. To illustrate this approach, a comparative two-dimensional numerical initial-boundary-value problem (IBVP) for the highly brittle aragonite (CaCO₃) is presented. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of fiber-reinforced PMMA at different scales

This paper deals with the modeling of fiber-reinforced PMMA. Focus is on the macroscopic mechanical response with emphasis on the fracture properties such as the ultimate strength and the fracture energy. In order to capture the macroscopic mechanical response of PMMA, a finite element formulation is presented. While the elastic response of the fibres and that of the surrounding matrix are modelled in standard manner, i.e., by standard bulk material models, the relevant failure modes such as cracking of the fibres are accounted for by means of the so-called Strong Discontinuity Approach (SDA). Since the fibres are relatively small, their fracture mechanical properties crucially depend on their geometry, i.e., they show a pronounced size effect. Based on numerical analyses of fibres with different geometries, the aforementioned size effect is naturally incorporated into the formulation [1]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inplane Stress Singularities at the Corner of an Anisotropic Material Discontinuity

In the mechanics of composite laminates the local mechanical inplane fields at corners of anisotropic material discontinuities are of particular interest since they can have singular behavior. In the present study, the stress and strain fields in the local near field of such corners are investigated by an asymptotic analysis. The order of the singularity of these mechanical inplane fields are determined in closed‐form manner by use of the complex potential method based on Lekhnitskii's approach. Various different geometrical setups and material combinations of corners with material discontinuities are investigated with regard to their effect on the singular behavior of the mechanical fields present. These examples show that the order of singularity considered is clearly weaker than the typical crack tip singularity in fracture mechanics. Nevertheless, it may render the corner a critical location for the onset of failure. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical investigations in structures with imperfect material interfaces and cracks

Natural fiber reinforced bio-polymers are in the focus of many research projects to understand and improve the mechanical behavior subjected to different process parameters during production. To provide safe and reliable light weight constructions, special interest is directed towards the damage and fracture behavior of such composite materials. Here, the material's behavior at the imperfect material interface between fiber and matrix plays an essential role and governs inelastic effects at the interfaces on the one hand, and the behavior of growing cracks on the other. The reduction of the elastic potential is related to both energy consuming processes in the system and in general is going along with a reduction of the crack tip loading and a shift of the crack growth direction. In this paper, the crack tip loading analysis in structures with perfect and imperfect material interfaces is presented and applied to different specimens. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Prediction of fracture in grain boundaries of nano-coatings using cohesive zone elements

A cohesive zone element technique (CZ) is applied to study grain boundary fracture in nano coating layers (see [1]). This goes along with the investigations of the delamination and fracture behavior of the coatings and the substrate interface. The main motivation is to investigate antiadhesive and wear resistant properties of coatings made of ceramics produced by the High Power Pulsed Magnetron Sputtering (HPPMS) technique [2]. Different physical conditions in HPPMS result into different grain morphologies with different mechanical properties. Therefore prediction of fracture and damage in such systems can lead to the optimum choice of process parameters in order to gain the best fracture resistance properties for the coatings. To illustrate the applicability of the model, several simulations with different mechanical and structural properties are performed. The developed CZ element model is capable of modeling the separation, the contact and also the irreversible reloading conditions in different directions [3]. The model is further developed to be applicable for geometrically complex interfaces including different bonding behaviors, with a high robustness. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Prediction of fracture toughness of embrittled steels by means of the Small Punch Test

To characterise the randomly distributed strength and fracture toughness of brittle steels, many specimens have to be destroyed. Since the Small Punch Test (SPT) needs only little material, it is a well suited experiment, when only a small volume of material is available. In this study the cleavage fracture of a ferritic steel at low temperature was investigated using the Beremin model. The failure probability is described with a 2-parameter Weibull distribution in terms of the so-called Weibull stress, which is calculated using an elastic-plastic finite element stress analysis. While the transfer of Weibull parameters works well between similar geometries and loading conditions, it works bad in more general cases. Modifications of the Beremin model are necessary to overcome this problem. Recent publications consider a lower threshold value of the Weibull stress, which leads to a lower Weibull modulus and therefore to a stronger volume size effect of strength. The suitability of this approach to transfer cleavage fracture results from SPT to fracture mechanics specimens was investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Energy dissipation in a glass laminate stressed in cyclic tension-compression

An experimental investigation has established that in a glass laminate most of the mechanical losses are converted into thermal energy. The sum of the mechanical losses increases with increase in the fatigue life of the material, the ratio of thermal losses remaining constant under given deformation conditions. Quantitative data are presented for the energy dissipation in various phases of the fatigue fracture process.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 655–661, July–August, 1969.     

Fractal materials, beams, and fracture mechanics

Continuing in the vein of a recently developed generalization of continuum thermomechanics, in this paper we extend fracture mechanics and beam mechanics to materials described by fractional integrals involving D, d and R. By introducing a product measure instead of a Riesz measure, so as to ensure that the mechanical approach to continuum mechanics is consistent with the energetic approach, specific forms of continuum-type equations are derived. On this basis we study the energy aspects of fracture and, as an example, a Timoshenko beam made of a fractal material; the local form of elastodynamic equations of that beam is derived. In particular, we review the crack driving force G stemming from the Griffith fracture criterion in fractal media, considering either dead-load or fixed-grip conditions and the effects of ensemble averaging over random fractal materials.     

Mathematical modelling of the development of mechanical instability in fracturing systems

The dynamics of processes accompanying a loss of stability in a mechanical system are investigated. The mechanical system is in the form of an elastic rod, stretched by an axial load, with one of its lateral surfaces “glued” to a rigid wall. The “glue” is a low-strength elastic material which is subject to brittle fracture at a certain value of the load acting on it. In a fractured segment, the rod surface slides over the wall surface under the action of a dry friction force which is less than the breaking stress. The high sensitivity of the process of the development of instability to small perturbations which initiate the development of instability is established. The system considered is the simplest model of the zone of contact between lithospheric plates which generate earthquakes.     

A composite material based on recycled tires

The present study is devoted to the elaboration and investigation of a composite material based on mechanically grinded recycled tires and a polymer binder. The correlation between the content of the binder, some technological parameters, and material properties of the composite was clarified. The apparent density, the compressive stress at a 10% strain, the compressive elastic modulus in static and cyclic loadings, and the insulating properties (acoustic and thermal) were the parameters of special interest of the present investigation. It is found that a purposeful variation of material composition and some technological parameters leads to multifunctional composite materials with different and predictable mechanical and insulation properties. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 145–150, January–February, 2009.     

Assessment of asymmetric crack initiation in open-hole plates using a coupled stress and energy criterion

An application of the finite fracture mechanics concept to open-hole plates subject to combined tensile and bending loading is presented. In finite fracture mechanics, the simultaneous satisfaction of both, a stress and an energy criterion, is enforced as a condition for crack initiation. Efficient modeling and closed-form expressions for the dependence of the stress and energy quantities on governing structural and material parameters allow for a comprehensive numerical analysis of the onset of asymmetric crack patterns. The obtained failure load predictions are found to agree well with a cohesive zone model and experimental data from literature. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New damage evolution model of rock material

As a kind of natural engineering material with original defects, there are distinctly nonlinear and anisotropic mechanical behaviors for rock materials. Nevertheless, the rock damage mechanics can solve this problem well. However, for the complexity of mechanical property of rock material, the mature and applicable model to describe the rock failure process and the method to determine the maximum damage value have not been established very well. To solve this problem, one new damage evolution model for rock material has been proposed. In this model, the least energy consumption principle proposed to describe the fracture process of materials is used. Using the experimental data of granite sample under uniaxial compression and the results of numerical tests under uniaxial tension and uniaxial compression, this model is verified. Moreover, the results of the new model have been compared with the results of the tests (numerical test and real test) and the traditional damage model. The comparison shows that the new model has the higher accuracy and better reflects for the fracture process of the granite sample. Moreover, the released damage energies of the new model and Mazars model are different, and the released damage energy of the new model is slightly less than that of the Mazars model.     

Multiscale modelling of skeletal muscle tissue by incorporating microstructural effects

The macroscopic mechanical response of skeletal muscle tissue is mainly influenced by the properties and arrangement of microstructural elements, such as, for example, sarcomeres and connective tissue. Like for many biological materials, the mechanical properties of skeletal muscle tissue can vary quite significantly between different specimens like, for example, different persons or muscle types. Current state-of-the-art continuum-mechanical muscle models often lack the ability to take into account such variations in a natural way. Further, phenomenological constitutive laws face the challenge that appropriate material parameter sets need to be found for each tissue variation. Thus, the present work aims to identify the microstructural features and parameters governing the overall mechanical response and to incorporate them into a macroscopic material model by applying suitable homogenisation methods. The motivation hereby is that the estimation of material parameters for microstructures, such as collagen fibres, can be done in a more reliable and general way and that fluctuations between specimens are included by, for example, adapting the alignment of the collagen fibres inside the muscle. Moreover, instead of computationally expensive homogenisation methods like FE², this work proceeds from well-founded analytical homogenisation techniques in order to keep the model as simple as possible. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Aerated autoclaved concrete: Stochastic structure model and elastic properties

Aerated autoclaved concrete (AAC) is a modern and important construction material, whose elastic properties are primarily defined by its porosity. The possibility to predict elastic properties of AAC based on the voids distribution is very important. The report describes simulations of the mechanical properties of AAC, based on a stochastic-geometric model of its structure. The model is the well-known “cherry-pit” model, which presents a random system of partially overlapping spheres. In the mechanical analysis the solid phase is approximated by a network model with the help of the so-called radical tessellation with respect to the hard spheres of the “cherry-pit” model. The network edges are modelled in ANSYS as 3D beams. In this approach, the discretized elements (the edges) have in distinction to FE calculations with small polyhedral same dimension as the air voids and so the numerical costs can be drastically reduced. The FE simulations calculate the elastic constants and energy concentrations, which are responsible for the material failures, in large samples. Comparisons with fracture tests showed good matching between simulations and experiments. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

八次对称二维准晶中的Ⅱ型裂纹

发展了八次对称二维准晶材料的断裂理论.应用Fourier变换与对偶积分方程理论,得到了八次对称二维准晶材料Ⅱ型Griffith裂纹的精确解析解,并由此确定了应力强度因子和应变能释放率,讨论了与相位子场有关结果的物理意义以及晶体与准晶体裂纹问题力学行为的差别,这些为研究此新固体材料的变形和断裂提供了重要的信息.     

Micromechanics of polymer fracture

Small-angle x-ray scattering has been used to investigate the formation of embryonic submicroscopic cracks in polymers under a load. The main characteristics of crack formation in various loading regimes are analyzed. It is shown that there is a relation between the submicrocrack concentration and the deformation of the loaded polymer. The principal parameters of crack formation determining the strength properties of the polymer are found to be the transverse dimension of the initial submicrocracks relative to the loading axis, which is determined by the structural heterogeneity of the material, and the submicrocrack concentration in the prefracture state. The principles of the micromechanics of polymer fracture are formulated on the basis of the results of an analysis of the quantitative relationship between these parameters. The dominant role of the surface in the fracture process is demonstrated by comparing the parameters of crack formation in the interior and at the surface of the loaded polymer.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 792–801, September–October, 1974.