Fracture Mechanics Parameters Research Articles

Research of nonlinear dynamic deformation of spatial bodies with cracks

The object of research is the process of dynamic interaction of a complex system of cyclically symmetric parts of the support joint, taking into account the presence of stationary cracks. A significant number of structural elements and parts operated under dynamic loads are characterized by the occurrence and propagation of cracks in areas of significant plastic deformation. In particular, for the supporting device, it is a cyclically symmetric body with a limiting case of heterogeneity, under the action of pulsed loads, plastic flow zones arise at the boundaries of the joints of the cylindrical part with projections. If there are cracks in these areas, it becomes necessary to reliably determine the fracture parameters and predict the crack growth over time.To build models of this class of objects, one of the most universal and reliable numerical methods is the semi-analytical finite element method.In this paper, the results of calculating of the parameters of fracture mechanics on the basis of the semi-analytical method of finite elements are presented for an object with inhomogeneous physical and mechanical properties in the presence of stationary cracks under conditions of pulsed loading and plastic deformations. The numerical study is performed in two stages. At the first stage, the laws of the elastic-plastic dynamic deformation of the system are established. The most probable zones of damage accumulation and cracking are determined, which is the reason for the failure of structural elements. At the second stage, a model with a crack located in the zone of plastic deformations is considered, the calculated values of the dynamic stress intensity factors are studied, and their evolution over time is investigated.The obtained research results can be used in numerous calculations of inhomogeneous bodies with damage such as cracks in the conditions of elastic-plastic dynamic deformations.

Non-Linear Analysis of an RC Beam Without Shear Reinforcement with a Sensitivity Study of the Material Properties of Concrete

Abstract A detailed analysis of concrete structures requires knowledge of the mechanical properties of the materials used. In the case of a non-linear analysis, the scope of the information needed is even greater. In particular, the tensile strength and fracture-mechanical parameters are required for the concrete. Prospective approaches that could increase the informative value of detailed analyses include the use of stochastic modelling. It particularly enables the definition of the effects of individual input parameters on the load capacity, failure mode, and general behaviour of the structure. The presented paper aims at a detailed analysis of a reinforced-concrete beam without shear reinforcement, which is based on a complex set of laboratory tests and non-linear analyses with a sensitivity study. The laboratory program includes different types of laboratory tests. Selected and missing material parameters of the concrete are calculated according to recommendations in scientific papers and the valid standards. The results are compared and discussed.

Effect of negative Poisson's ratio on the fracture mechanics parameters due to mechanical and thermal loads

The objective of the paper is to study the effect of negative Poisson's ratio on the crack tip field under the application of external mechanical load and temperature. Explicit and analytical expressions for the fracture mechanics parameters such as stress intensity factors and the energy release rate are obtained. The expressions for the thermal loads are derived in axisymmetric cylindrical coordinates under the framework of steady-state uncoupled linear thermoelasticity. Numerical results are presented graphically to demonstrate the effect of negative Poisson's ratio on the crack tip field. The results show that for the case of applied mechanical loads, materials with negative Poisson's ratio have higher energy release rate. However, if the applied are thermal loads, the crack tip fracture mechanics parameters are significantly decreased.

The concept and numerical evaluation of M-integral based on domain integral method in cracked viscoelastic materials

A new form of M-integral associated with time dependence parameters, is presented herein for viscoelastic materials. Based on the equivalent domain integral method, this time-dependent M-integral is numerically implemented as an effective and accepted fracture mechanical parameter for damage induced by crack growth in viscoelastic materials. Based on the linear viscoelastic model defined through Prony series, the conservation of the time-dependent M-integral for viscoelasticity is verified by applying user defined Python scripts. The results show that the newly proposed time-dependent M-integral can be successfully calculated numerically. Furthermore, numerical examples are given to demonstrate the validity and relevance of the time-dependent M-integral in viscoelastic material. In particular, the variations of the time-dependent M-integral for different loading rates are considered, which show that the crack growth behavior over a period of time in viscoelastic material can be evaluated based on the value of the time-dependent M-integral. In addition, the time-dependent M-integral is calculated to assess the damage degree induced by two collinear cracks.

Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures

Creep damage and creep crack growth (CCG) behavior of Crofer 22 APU as interconnect of solid oxide fuel cell at different temperatures are investigated by the continuum damage mechanics method through CT specimen. It is illustrated that the fracture time of CT specimen reduces with temperature increasing at the same stress level, they are 1297 h, 42 h, 1.8 h and 0.25 h, respectively, at 650, 700, 750 and 800 °C with stress level of 2.73 MPa⋅m. The slopes of creep fracture mechanics parameter C* to CCG rate a˙ (C*- rate of a) are nearly the same at 650 and 700 °C. The slope of C*- a˙ at 650 and 700 °C is smaller than that at 750 and 800 °C. It is concluded that the temperature effect on CCG behavior of Crofer 22 APU is more evident than that the stress effect. All the data of C*- a˙ fall within the area of 95% prediction band, and the obtained equation of C* and CCG rate is a˙=3.8e2C∗0.91. Therefore, the a˙ of Crofer 22 APU can be predicted under different stress levels and temperatures.

The T-stress influence on the plastic zone size around the crack tip under the thermal load

A review of the fracture mechanics problems for estimating the safety of constructions with the crack-like defects is carried out. The need to develop a new methodology that combines the advantages of calculation and instrumental methods was revealed. The correlations between the most important fracture mechanics parameters and the characteristics of acoustic-emission signals proposed to use for estimating the parameters of stress-strain state. It is noted that considerable attention should be paid to the size and shape of the plastic zone in order to establish a theoretical relationship between the characteristics of acoustic signals and the fracture mechanics parameters. It is assumed that T-stresses are the cause of differences in the coefficients of the power dependence of the parameters of acoustic signals for the same values of the stress intensity factor. The task of finding the influence of T-stresses on the size of the plastic zone at the crack tip is set. A numerical modeling of thermal loading of a steel sheet with a central crack by the finite element method is carried out in order to determine the dependence of the crack tip plastic zone size on the stress intensity factor for several values of T-stress. Multiple calculations of the stress intensity factor and the T-stresses were performed for the several values of the cooling zone, using the parametric design language ANSYS APDL. By substituting the yield point of the material into the equations of linear elastic fracture mechanics, the specific volume and linear plastic zone size along the crack line were determined for the previously found values of the stress intensity factor and T-stress. A relationship between the fracture mechanics parameters and the plastic zone size at the crack tip was established using numerical methods. The assumptions that the T-stress influence to the plastic zone size are qualitatively confirmed. It is shown, that the negative values of T-stresses decrease the plastic zone size for a same value of the stress intensity factor.

Complex multilevel fracture tests of concrete: basic mechanical fracture parameters of standard size specimens

The aim of the current research is to develop a complex multilevel approach for the experimental–computational determination of mechanical fracture parameters of concrete as a typical quasi-brittle material. This includes testing, advanced evaluation and soft computing-based identification of specimens of multiple sizes in multiple test configurations and analyses of fracture processes using multiscale modelling approaches. The evaluation of a part of an extensive experimental program is presented in this paper. The basic mechanical fracture parameters of the investigated concrete determined on standard test specimens with nominal dimensions of 100 × 100 × 400 mm subjected to the standard three-point bending fracture test are introduced. The results of three different sets of specimens provided with different depths of the initial notch are compared in terms of absolute values of the selected mechanical fracture parameters. The results indicate different sensitivity of particular mechanical fracture parameters in relation to the depth of the initial notch.

Characteristic Tensor for Evaluation of Singular Stress Field under Mixed-mode Loadings

A characteristic tensor is defined using stress tensor averaged in a small circular domain at the crack tip and multiplied by the root of domain radius. It possesses the original stress tensor characteristics and has a simple relationship with conventional fracture-mechanics parameters. Therefore, it can be used to estimate stress intensity factors (SIFs) for cracks of arbitrary shape subjected to multiaxial stress loads. A characteristic tensor can also be used to estimate SIFs for kinked cracks. This study examines the relation between a characteristic tensor and SIFs to demonstrate the correlation between the characteristic tensor and fracture-mechanics parameters. Consequently, a single straight crack and a kinked crack of finite length existing in a twodimensional, infinite isotropic elastic body in a plane stress state, were considered to investigate the properties of the characteristic tensor under mixed-mode loadings. To demonstrate the practical utility of the characteristic tensor, the stress distribution obtained through finite element analysis (FEA) was used to estimate mixed-mode SIFs, and the values of estimated SIFs were compared with those obtained using an analytical solution. Results demonstrate that SIFs estimated under mixed-mode loadings exhibit a good agreement with the analytical values. This indicates that the proposed characteristictensor-based approach is effective in extracting features of singular stress fields at crack tips, and can be employed to estimate values of fracture-mechanics parameters, such as SIFs. Owing to its simplicity, the proposed approach can be easily incorporated in commercial FE codes for practical applications to simulate the crack-growth problem under both static and dynamic loading scenarios. The excellent applicability of the characteristic tensor greatly contributes to efficiency of the design process in industries.

Material Effects on Risk Assessment of Residual Life of Oil Drilling Rig Pipe

Fracture mechanics parameters are used for numerical and analytical risk assessment of residual life of a cracked oil drilling rig welded pipe. Number of cycles to the critical crack length, obtained by direct integration of Paris law, verified by using extended Finite Element Method, are related to the number of cycles needed for 10 years of exploitation, to assess probability and risk due to fatigue crack growth.

Lifetime Assessment for a Cracked Compressor Disk Based on the Plastic Stress Intensity Factor

Based on a new fracture mechanics parameter, this study is concerned with assessment of the lifetime of a cracked aircraft gas turbine engine compressor disk operating under low cyclic loading conditions. In combination with the elastic-plastic properties of the VT3-1 titanium alloy, various combinations of angular velocity, temperature, surface flaw form and size are considered. A lifetime prediction model, which is based on the fracture process zone size and plastic stress intensity factor (SIF), is proposed. The durability of the compressor disk is predicted on the basis of SIF distributions obtained from elastic and plastic crack growth models.

T-Stress on a cruciform specimen: A preliminary study for a new crack propagation model

Mixed mode fatigue crack growth (FCG) can occur due to complex loading or specimen geometry. Fatigue crack paths can be determined using propagation criteria like the Maximum Tangential Stress (MTS) criterion, or the Maximum Shear Stress (MSS) criterion, for mode I and II dominated propagation respectively. These criteria only consider mode I and II Stress Intensity Factors (SIF), neglecting the T-Stress effects. In order to develop a new fatigue crack propagation model, that takes this fracture mechanics parameter into account, T-Stress values on a cruciform specimen were calculated for different loading conditions. Using a previously developed Finite Element Analysis (FEA) automatic propagation algorithm, cracks with two different initial orientations, were allowed to grow under different biaxial loading ratios and phases. Also, two holes were simulated on the specimen, in order to assess their influence on FCG. The resulting T-Stress values were determined as a function of the loading conditions and compared with the crack paths. It was possible to correlate the T-stress values with crack propagation direction stability and loading parameters, enabling the future development of a new crack propagation model, considering the influence of this fracture mechanics parameter.

Automatic prediction of the fatigue crack trajectory in plane finite element models

A module for automatic prediction of the fatigue crack trajectory in plane finite-element models in Ansys APDL software package was developed. Crack propagation is modeled by exclusion of elements from the active set in the direction, which is determined based on criterion of the maximum energy flux to the crack tip. The module determines the parameters of fracture mechanics (stress intensity factor and J-integral) at each step of crack propagation.

Development of a special specimen geometry for the experimental determination of fracture mechanical parameters of clinchable metal sheets

In order to reduce the energy demand and harmful emissions of moving masses, lightweight construction is becoming increasingly important. In many areas of product manufacturing the constructions consist of individual components and sheets that are joined together to form complex structures. Due to the simplicity of the process, clinching without auxiliary joining parts or pre-holes is often used. The utilized sheets are usually less than 2 mm thick and possibly characterized by anisotropy in the mechanical material properties because of different rolling directions. The sheets are arranged in an overlapping and partially interspersed way, so that impact extrusion results in an inseparable connection between the components made of the same or even different materials. During the joining process and due to the service load, cracks can occur in the area of the joint, propagate due to cyclic loading and consequently lead to structural failure. Within the scope of this paper experimental and numerical preliminary tests for the fracture mechanical characterization of the metal sheets used in the clinching process as well as first crack growth rate curves are presented. In order to determine the fracture mechanical parameters of the base material, the development of a new specimen geometry is necessary due to the low sheet thickness. The numerical calculation of the geometry factor function as well as the calibration function of this special specimen geometry enables the determination of the crack growth rate curves. Following the experimental validation of the numerically determined calibration function, crack growth rate curves are determined for the stress ratio R = 0.1. Furthermore, different rolling directions and further R-ratios are considered in the experimental investigations to examine the influence of the anisotropy arising during rolling and the mean stress sensitivity.

Experimental and numerical analysis of the fracture response of alkali-activated slag-based materials

The paper deals with the experimental and numerical determination of mechanical fracture parameters of fine-grained composites based on the alkali-activated slag (AAS) at different ages of hardening. Two AAS composites, which differed only in the presence of shrinkage reducing admixture, were studied. The prismatic specimens with the nominal dimensions of 40 × 40 × 160 mm and initial central edge notch were subjected to fracture tests in a three-point bending configuration. The results of the fracture tests in the form load F versus deflection d diagrams were used as input data for the identification of parameters via the inverse analysis based on the artificial neural network whose aim is to transfer the fracture test response data to the desired material parameters. The modulus of elasticity, tensile strength, and fracture energy values were identified and subsequently compared with values obtained based on the direct fracture test evaluation using the effective crack model and work-of-fracture method.

Time-dependent fracture of epoxy resin under mixed-mode I/III loading

In this study, fracture behavior of epoxy resin under mixed-mode loading between opening mode (mode I) and out-of-plane shearing mode (mode III) was investigated using an adjustable loading fixture set with a single-edge notched tension (SENT) specimen. Effects of specimen thickness and loading rate were investigated. Two different thicknesses of specimen were employed (4 and 8 mm) And, the fracture toughness tests were performed at two different loading rates of 0.1 and 1000 mm/min. Fracture toughnesses of epoxy resin were calculated using finite element (FE) analysis based on both linear-elastic fracture mechanics (LEFM) and elastic–plastic fracture mechanics (EPFM). It was found that under mixed-mode I/III and pure mode III loadings, fracture occurred in a ductile manner with severe plastic deformation. Therefore, LEFM is no longer valid, and EPFM approach was applied in this study to characterised fracture behavior of epoxy resin under mixed-mode I/III loading. Two different fracture mechanics parameters based on EPFM, e.g. critical J-integral (Jc) and critical crack-tip displacement, were calculated. Jc results revealed that the effect of specimen thickness was significant at low loading rate. However, at high loading rate the effect of specimen thickness was marginal. While, critical crack-tip displacement results indicated that fracture occurred at the same level of crack-tip displacements regardless of specimen thickness. An observation of fracture surfaces agreed with the crack-tip displacement results, i.e., a similar fracture surface topology for both thick and thin specimens tested at the same loading rate.

Tabulated solutions of stress intensity factor and elastic crack opening displacement for elbow joints with practical through-wall cracks

Various fracture mechanics parameters should be considered for elbow design and leak-before-break assessment. In the case of a pipe with through-wall cracks (TWCs), the stress intensity factor (SIF) and elastic crack opening displacement (COD) are among the most important factors. Many studies have determined the SIF and elastic COD for idealized TWC straight and elbow pipes. However, no study has considered realistic crack geometries occurring in elbow joints. Thus, the objective of this study was to accurately predict the SIF and elastic COD of elbow joints by developing a three-dimensional finite element (FE) model for practical TWC (P-TWC). The developed FE model was then verified through comparisons with existing SIF and elastic COD solutions for idealized TWCs in elbow joints. In addition, tabulated solutions for the SIF and elastic COD were proposed by considering practical crack-geometry ranges and various loading conditions.

Influence of artificial aggregate on mechanical properties, fracture parameters and bond strength of concretes

The paper presented herein investigates the mechanical performance of concrete involving lightweight and normal weight aggregates with similar compressive strength. For this, two compressive strength values, 25 and 45 MPa, were considered for the concretes produced by normal and lightweight aggregates. Therefore, four concrete mixtures were designed at different water-to-cement ratios and cement contents. The lightweight aggregate utilized in this study was produced through cold bonding pelletization of fly ash and cement at ambient temperature in a specially designed tilted pan. The artificial lightweight aggregate used as a substitution of natural aggregate had similar particle size distribution to that of natural aggregate. The same mixing procedure was adopted to produce concrete and the testing specimens attained from each mixture were cured at the same circumstances. After the 28-day curing period, the specimens were tested for compressive strength and modulus of elasticity, splitting tensile and flexural strengths. Moreover, advanced mechanical properties such as fracture parameters, bond strength between embedded reinforcement and the concrete were also investigated. The test results indicated that it is possible to produce the lightweight aggregate concrete having similar compressive strength with the natural aggregate concrete, however, the utilization of artificial lightweight aggregates significantly influenced the investigated mechanical and fracture properties of the concretes despite having the similar compressive strengths. But, it was also observed that the utilization of lightweight aggregate made the concrete more ductile.

Factors determining characteristics of crack resistance of concrete structures

Despite the fact that concrete and reinforced concrete are the main construction materials, to date there is no complete theory of deformation and destruction. Structural concrete is considered at the level of macrostructure, has a number of features that do not allow you to directly transfer some of the provisions obtained for homogeneous materials. Available experimental data on the resistance of the concrete crack propagation relate mainly to the laboratory samples. In the paper, a new method for obtaining the fracture mechanics parameters of concrete, which is one of the most promising areas of research of fracture of composite materials. The study investigates the characteristics of cracks at different parameters of the segment breaks off. The study was carried out on finite element models. The authors studied the influence of the tilt angles formed by the segment on the stress state at the tip of the crack. In addition, the research separately considered the changes in mechanical properties of a break-off segment. As a result, the authors built regression tables and graphs. In conclusion, the research provides recommendations for the implementation of a shape for the break-off segment.

Prediction of the Ceramic Foam Structure Failure Using a Detailed Finite Element Model

The contribution deals with modelling and prediction of failure of mechanically loaded open cell ceramic foam structures by using 3D volume FE models constructed from CT scans of real foam specimens. The condition for crack initiation in particular struts comes from the coupled stress-energy criterion which combines two fracture-mechanics parameters of the investigated material – tensile strength and its fracture toughness. By combining of both stress and energy condition one obtains information about the crack initiation length which is later used (together with the tensile strength) for determination of the strut failure in the complex 3D FE model of the ceramic foam structure. The crack onset is considered in the critical location at the moment when the (tensile) principal stress under the strut surface (in a depth corresponding to the crack initiation length) exceeded the tensile strength of the strut. Such approach enables us to define failure also on relatively coarse meshes of the FE models where potential stress concentrations are not described precisely and therefore it is not possible to decide about the failure just based upon the value of tensile stress on the strut surface.

Composites fatigue delamination prediction using double load envelopes and twin cohesive models

This paper presents an explicit finite element methodology for predicting fatigue delamination in composite laminates using twin cohesive models and a combined static & fatigue cohesive formulation; one model is loaded under the peak-load envelope, whilst the other model is loaded under the trough-load envelope. The twin models contain pairs of twin cohesive interface elements that predict delamination growth by exchanging data at every time increment. The cohesive formulation evaluates fracture mechanics parameters, e.g. the local minimum to maximum fracture energy ratio via local information associated with the twin cohesive elements, without the need to know the global loading information, e.g. the global R ratio. The method allows predicting the mechanical condition of a laminate at both the peak and trough loads. This method is validated by multiple test cases with varying mode mixities and R ratios, showing a high computation efficiency.