Analysis of fracture initiation angle in some cracked ceramics using the generalized maximum tangential stress criterion

Brittle fracture in ceramics sometimes occurs under combined opening-sliding (or mixed mode I/II) crack deformation. In this paper, a generalized maximum tangential stress criterion is employed for predicting the fracture initiation angle under mixed mode I/II loading in some brittle ceramics including alumina, zirconia, soda lime glass and three silicon based ceramics. The experimental results reported for the fracture angles in these ceramics have been obtained from fracture tests on the centrally cracked circular disc (often called the Brazilian disc). Very good agreement is shown to exist between the experimental results and the theoretical predictions. According to the fracture model, the mixed mode fracture angle is strongly dependent on the elastic T-stress in the tested ceramics. The negative T-stress that exists in the Brazilian disc specimen can be the main influencing parameter for decreasing the fracture initiation angle in the investigated ceramics.     

Mixed mode fracture in epicycloid specimens iii. Dislocations

Complex stress potentials are derived to obtain an analytical solution for the stresses in epicycloidal specimens which contain a dislocation. The solution is used to obtain an analytical expression for the stress intensity factors of cusp-like cracks in such specimens which can be considered as a generalization of the well established concept of Griffith cracks. It is shown that by suitable positioning of the dislocation, both positive and negative mode I stress intensity factors will result. This illustrates the potential of epicycloid specimens for determination of fracture properties under compressive loading where frictional contact of the crack surfaces is a priori avoided.     

Fracture prediction in stretch forming using finite element simulation combined with ductile fracture criterion

Summary  A criterion for ductile fracture is introduced in the finite element simulation of sheet metal forming. From the calculated histories of stress and strain in each element, the fracture initiation site and the critical stroke are predicted by means of the ductile fracture criterion. The calculations are carried out for axisymmetric stretch forming of various aluminium alloy sheets and their laminates clad by mild steel sheets. The predictions so obtained are compared with experimental observations. The results show that the combination of the finite element simulation and the ductile fracture criterion enables the prediction of forming limit in a wide range of sheet metals. Accepted for publication 11 August 1996     

On the correctness of the energy criterion in fracture mechanics

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 10, pp. 28–34, October, 1995.     

A micromechanics-based modification of the Gurson criterion by using Eshelby-like velocity fields

In this study, we propose a micromechanics-based modification of the Gurson criterion for porous media subjected to arbitrary loadings. The proposed formulation, derived in the framework of limit analysis, consists in the consideration of Eshelby-like exterior point trial velocity fields for the determination of the macroscopic dissipation. This approach is implemented for perfectly plastic rigid von Mises matrix containing spherical voids. After the minimization procedure required by the use of the Eshelby-like trial velocity fields, we derive a two-field estimate of the macroscopic yield function. It is shown that the obtained closed-form estimate provides a significant modification of the Gurson criterion, particularly in the domain of low stress triaxialities. This estimate is first compared with existing criteria. Moreover, its accuracy is assessed through comparison with results derived from numerical exact two-field criterion and with recently available numerical bounds.     

Dual-parameter elastic-plastic fracture criterion of metals and alloys in the plane strain case

In recent years, some investigators discussed the applicability of the HRR theory for engineering materials based on the results of numerical analyses and experimental studies. In the present paper, the finite element method is employed to analyze the crack tip fields of the engineering elastic-plastic material with a variety of geometry configurations of cracked specimens from elastic state to intensely general yielded state in the plane strain case. The results indicate that the HRR theory loses its validity of application for engineering elastic-plastic materials in the plane strain case. The reasons for this are analyzed. A dual-parameter fracture criterion is suggested for this case.     

Analytical investigation of nonlinear interlaminar fracture in trilayered polymer composite beam under mode II crack loading conditions using the J -integral approach

The present study is concerned with a nonlinear fracture analysis of trilayered beam built up by two unidirectional fiber-reinforced polymer composites. It is assumed that two interlaminar cracks exist between the layers. A tensile force applied to the middle layer generates pure mode II crack loading conditions. The J -integral approach is used to investigate the nonlinear fracture behavior of the beam. The elastic-linearly hardening model is applied to describe the mechanical behavior of the two composites. Sixth expressions for J -integral are derived using a beam theory model. These expressions correspond to the characteristic magnitudes of the external force. The validity of the formulae obtained is proved by comparison with the J -integral solution in the case of linear-elastic behavior of the composite materials. A numerical example is presented in order to demonstrate the ability of the expressions obtained for the analysis of nonlinear fracture in polymer composites.     

Application of a stress triaxiality dependent fracture criterion in the finite element analysis of unnotched Charpy specimens

Nonlinear dynamic finite element analysis (FEA) is conducted to simulate the fracture of unnotched Charpy specimens of steel under pendulum impact loading by a dedicated, oversized and nonstandard Bulk Fracture Charpy Machine (BFCM). The impact energy needed to fracture an unnotched Charpy specimen in a BFCM test can be two orders of magnitude higher than the typical impact energy of a Charpy V-notch specimen. To predict material failure, a phenomenological, stress triaxiality dependent fracture initiation criterion and a fracture evolution law in the form of strain softening are incorporated in the constitutive relations. The BFCM impact energy results obtained from the FEA simulations compare favorably with the corresponding experimental data. In particular, the FEA predicts accurately the correlations of the BFCM impact energy with such factors as specimen geometry, impactor tup width and material type. The analyses show that a specimen’s progressive deterioration through the thickness dimension displays a range of shear to ductile fracture modes, demonstrating the necessity of applying a stress state dependent fracture initiation criterion. Modeling the strain softening behavior helps to capture the residual load carrying capability of a ductile metal or alloy beyond the onset of damage. The total impact energy can be significantly under predicted if a softening branch is not included in the stress-strain curve. This research supports a study of the puncture failure of railroad tank cars under dynamic impact loading. Applications of the presented fracture model in failure analyses of other structures are further discussed.     

Optimizing energy input for fracture by analysis of the energy required to initiate dynamic mode I crack growth

A problem for a central crack in a plate subjected to plane strain conditions is investigated. Mode I crack loading is created by a dynamic pressure pulse applied at large distance from the crack. It was found that for a certain combination of amplitude and duration of the pulse applied, energy transmitted to the sample has a strongly marked minimum, meaning that with the pulse amplitude or duration moving away from the optimal values minimum energy required for initiation of crack growth increases rapidly. Results received indicate a possibility to optimize energy consumption of different industrial processes connected with fracture. Much could be gained in for example drilling or rock pounding where energy input accounts for the largest part of the process cost. Presumably further investigation of the effect observed can make it possible to predict optimal energy saving parameters, i.e., frequency and amplitude of impacts, for industrial devices, e.g., bores, grinding machines, etc. and hence significantly reduce the process cost. The prediction can be given based on the parameters of the media fractured (material parameters, prevalent crack length and orientation, etc.).     

Eigenproblems of two-dimensional acoustic cavities with smoothly varying boundaries by using the generalized multipole method

This paper presents a semi-analytical approach to solve the eigenproblem of a two-dimensional acoustic cavity with smoothly varying boundaries. The multipole expansion for the acoustic pressure is formulated in terms of Bessel and Hankel functions to satisfy the Helmholtz equation in the polar coordinate system. Rather than using the addition theorem, the multipole method and directional derivative are both combined to propose a generalized multipole method in which the acoustic pressure and its normal derivative with respect to non-local polar coordinates can be calculated. The boundary conditions are satisfied by uniformly collocating points on the boundaries. By truncating the multipole expansion, a finite linear algebraic system is acquired. The direct searching approach is applied to identify the natural frequencies using the singular value decomposition technique. Several numerical examples are presented, including those of an annulus cavity, a confocal elliptical annulus cavity and an arbitrarily shaped cavity with an inner elliptical boundary. The accuracy and numerical convergence of the proposed method are validated by comparison with results of the available analytical method and the commercial finite-element code ABAQUS. No spurious eigensolutions are found in the proposed formulation. Due to its semi-analytical character, excellent accuracy and fast rate of convergence are the main features of the proposed method.     

Sufficient criterion of fracture in the case with a complex stress state and non-proportional deformation of the material in the pre-fracture zone

A general case of proportional loading with a complex stress state of the material in the pre-fracture zone, which is typical for polycrystalline solids with plastic deformation, is considered. A sufficient criterion of fracture is proposed for the case of a complex stress state with non-proportional deformation of the material in the pre-fracture zone. Critical parameters of fracture (pre-fracture zone length and load) for cracks propagating in quasi-brittle materials are obtained with the use of a modified Leonov-Panasyuk-Dugdale model. The pre-fracture zone width is determined by solving the problem of the plasticity theory in the vicinity of the crack tip. The proposed modification of the Leonov-Panasyuk-Dugdale model makes it possible to estimate the critical opening of the crack and the critical displacement of the crack flanks. Inequalities that describe different mechanisms of material fracture under proportional loading (predominantly shear fracture mechanism and fracture mechanism through cleavage) are derived.     

Analysis methods and size effects in the indentation fracture toughness assessment of very thin oxide coatings on glass

Very thin oxide coatings (<100 nm) which are used as anti-reflection and barrier layers in low emissivity architectural glass have been studied by nanoindentation methods to determine the effect of coating thickness on fracture toughness. Traditional microindentation-derived methods to determine the fracture toughness are unsuitable for assessing very thin coatings (<500 nm) and alternative energy-based models are required depending on what features are visible in indentation load–displacement curves. In cases where radial cracks are formed and grow in a discontinuous manner there are excursions in the load–displacement curve which can be the basis for analysis. In cases where picture frame cracks are observed there are no such features and an alternative approach based on assessment of irreversible work of indentation is required. This paper reviews the methods for obtaining fracture toughness data for very thin coatings and assesses the existence of size effects in the mechanical response of oxide coatings with different thickness on a glass substrate. For oxide coatings in the thickness range 100 to 400 nm no size effects in fracture toughness were observed.     

Improving the differentiability of generalized fourier series solutions of boundary value problems of mechanics by using boundary functions

We prove a theorem on conditions for the differentiation of generalized Fourier series. We show that Fourier series solutions of boundary value problems can in general be differentiated term by term only once. To improve the differentiability properties of such series, we suggest to use pth-order boundary functions. We suggest an algorithm for constructing boundary functions for classical domains. This approach is illustrated by a new solution, with improved differentiability properties, of the problem on the torsion of an elastic rod of rectangular cross-section.     

Investigation of the elastoplastic deformation and the fracture criterion of a transversally isotropic material subject to uniaxial compression in a direction parallel to the isotropy plane

The stress-strain state and fracture of a transversally isotropic material subject to uniaxial compression in a direction parallel to the isotropy plane is studied. The deformation theory of the plasticity of a transversally isotropic body was used to analyze the stress-strain state. The fracture analysis of the material is carried out using a proposed variant of the strain-strength criterion. Theoretical and experimental data on the stress-strain state and the strength of a transversally isotropic material are compared. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 67–71, March, 2000.     

Delamination fracture analysis in the GII–GIII plane using prestressed transparent composite beams

In this paper, the mixed-mode II/III version of the prestressed end-notched flexure fracture specimen is developed, which combines the well-known end-notched flexure and the modified split-cantilever beam specimens using a special rig. The new beam-like specimen is able to provide any combination of the mode-II and mode-III strain energy release rates. The mode-III part of the strain energy release rate is fixed by using the special rig, which loads the specimen in the plane of the delamination. The mode-II part of the strain energy release rate is provided by the external load using a three-point bending fixture. A simple closed-form solution using beam theory is developed for the strain energy release rates of the new configuration. The applicability and the limitations of the novel fracture mechanical test are demonstrated using unidirectional E-glass/polyester composite specimens. If only crack propagation onset is involved then the mixed-mode II/III prestressed end-notched flexure specimen can be used to obtain the fracture criterion of transparent composite materials in a relatively simple way.