Stochastic model for the size distribution of dispersed cracks. Part 1. Steady-state crack growth

Multiple fracture of loaded material surfaces is examined; under these conditions two major damage processes simultaneously take place: initiation and propagation of small dispersed cracks. The initiation of cracks was simulated as a Poisson point process with constant and time-dependent intensities. The propagation of cracks with a random velocity was described by a linear length-time function. Different types of crack growth rate distributions are examined: uniform and gamma, including the exponential one. The statistical distributions of dispersed crack lengths are similar, and in the reduced form they can be described by a generalized exponential function. Kiev International University of Civil Aviation, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 104–113, May–June, 1999.     

A fatigue crack initiation model incorporating discrete dislocation plasticity and surface roughness

Although a thorough understanding of fatigue crack initiation is lacking, experiments have shown that the evolution of distinct dislocation distributions and surface roughness are key ingredients. In the present study we introduce a computational framework that ties together dislocation dynamics, the fields due to crystallographic surface steps and cohesive surfaces to model near-atomic separation leading to fracture. Cyclic tension–compression simulations are carried out where a single plastically deforming grain at a free surface is surrounded by elastic material. While initially, the cycle-by-cycle maximum cohesive opening increases slowly, the growth rate at some instant increases rapidly, leading to fatigue crack initiation at the free surface and subsequent growth into the crystal. This study also sheds light on random local microstructural events which lead to premature fatigue crack initiation.     

Crack growth kinetics in three-dimensional polymethyl methacrylate specimens under internal dynamic loading

Literature data and our experimental results obtained in the studies on crack kinetics in three-dimensional polymethyl methacrylate specimens with an inner cavity made in various shapes over a wide range of loading rates are summarized. Crack initiation and steady propagation velocities as well as energy spent for fracture are found to increase nonlinearly, and the delay time of crack initiation decreases with the rate of internal cavity loading. Subbotin Institute of Geophysics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 86–94, January–February, 1999.     

Estimation of dynamic fatigue strengths in brittle materials under a wide range of stress rates

This paper aims to statistically estimate the dynamic fatigue strength in brittle materials under a wide range of stress rates. First, two probabilistic models were derived on the basis of the slow crack growth (SCG) concept in conjunction with two-parameter Weibull distribution. The first model, Model I, is a conventional probabilistic delayed-fracture model based on a concept wherein the length of the critical crack growth due to SCG is enough larger than the initial crack length. For the second model, Model II, a new probabilistic model is derived on the basis of a concept wherein the critical cracks have widely ranging lengths. Next, a four-point bending test using a wide range of stress rates was performed for soda glass and alumina ceramics. We constructed fracture probability–strength–time diagrams (F–S–T diagrams) with the experimental results of both materials using both models. The F–S–T diagrams described using Model II were in good agreement with plots of the fracture strength and the fracture time of both materials more so than Model I.     

Creep crack growth in joints of a thermoplastic

An investigation of creep crack growth in butt heat fusion joints in a high density polyethylene (HDPE) is performed to quantify their life expectancy. Three point bend specimens containing a centrally located notched joint are used in creep crack growth tests at ambient and elevated temperatures. A quasi-nonlinear viscoelastic fracture mechanics model is used to deduce the crack growth histories from the measured load-point displacement histories. The initiation time for crack growth and the rate of crack growth are correlated with the stress intensity factor for combinations of initial crack lengths, applied loads and test temperatures. The elevated temperature data are shifted bidirectionally, utilizing shift functions derived from stress relaxation tests, to develop master curves for the initiation time and rate of crack growth. These master curves are used to predict the life of a girth joint containing an initial circumferential surface crack extending through 10 percent of the thickness of a pressurized pipe.     

Crack growth in the process of unstable brittle fracture

We suggest a model of the transition of a crack from stable to unstable propagation with subsequent growth in the supercritical state. By using the energy balance equation for propagating cracks, we estimate the specific surface energy and crack growth rate under the conditions of unstable propagation. Unstable propagation starts with a rate which is lower than the maximum crack growth rate in the material. The specific surface energy and kinetics of the crack undergoing unstable fracture depend both on the maximum crack growth rate in the material and on the initial rate υ₀ of its unstable propagation. The rate υ₀ is largely determined by the critical size of the crack (critical stresses). Blagonravov Institute of Mechanical Engineering, Russian Academy of Sciences, Moscow. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 6, pp. 81–86, November–December, 1996.     

On investigation of the kinetics of small surface cracks in light alloys under high-frequency loading

For the case of cyclic loading of metal materials in the frequency range from 100 to 10,000 Hz, we propose a method of studying small crack growth using a system of measuring the response of a defect section of material to the action of a high-frequency electromagnetic field. We present approaches to the construction of a measuring system for determination of the length of small surface cracks propagating from an introduced initial defect and formulate requirements for the choice of geometrical parameters of an initial concentrator. With the cyclic stress level being equal, short fatigue cracks (about 0.1 to 0.2 mm), have been found to originate sooner (with respect to the number of cycles to fracture) at a higher loading frequency. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2 pp. 67–74, March–April, 2000.     

Fatigue crack initiation and propagation under cyclic contact loading

A computational model for contact fatigue damage analysis of gear teeth flanks is presented in this paper. The model considers the conditions required for the surface fatigue crack initiation and then allows for proper simulation of the fatigue crack propagation that leads to the appearance of small pits on the contact surface. The fatigue process leading to pitting is divided into crack initiation and a crack propagation period.The model for prediction of identification of critical material areas and the number of loading cycles, required for the initial fatigue crack to appear, is based on Coffin-Manson relations between deformations and loading cycles, and comprises characteristic material fatigue parameters. The computational approach is based on continuum mechanics, where a homogenous and elastic material model is assumed and results of cyclic loading conditions are obtained using the finite element method analysis.The short crack theory together with the finite element method is then used for simulation of the fatigue crack growth. The virtual crack extension (VCE) method, implemented in the finite element method, is used for simulating the fatigue crack growth from the initial crack up to the formation of the surface pit. The relationship between the stress intensity factor K and crack length a, which is needed for determination of the required number of loading cycles N_p for a crack propagation from the initial to the critical length, is shown.     

A unified model of initiation and growth of fatigue macrocracks. part 3. stage of growth of a macrocrack

From a common viewpoint, fatigue fracture of materials is simulated by the process of initiation of an initial macrorack of lengtha _i =d ^* (d ^* is the constant of the material), which is successively (stepwise) repeated at the stage of its growth. As a result, the diagram “range of local stresses-period of initiation of an initial macrocrack” or ”range of local strains-period of initiation of an initial macrocrack,” which was determined for notched specimens, can be used for the construction of the diagram “growth rate of a macrocrack-range of the stress intensity factor” or “growth rate of a macrocrack-range of local strains,” respectively, if the crack is presented as a sharp notch with effective rounded radius ρ_eff=d ^* of the tip. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 3, pp. 5–14, May–June, 1999.     

Prediction of fracture characteristics of metals from high-frequency test data

A method is proposed for the prediction of cyclic crack resistance characteristics of metallic materials under low-frequency loading from high-frequency test data, which is based on a model of development of local plastic deformation regions during the accumulation of fatigue damages and fatigue crack growth with allowance for cyclic loading rate. We performed a comparative analysis of the results of prediction of fatigue fracture diagrams with test data for VT22, VT18U, VNS-25, and AMg6N alloys in a frequency range of 20 Hz–10 kHz. Report on International Conference “Dynamics, Strength, and Life of Machines and Structures” (1–4 November 2005, Kiev, Ukraine). __________ Translated from Problemy Prochnosti, No. 2, pp. 121–128, March–April, 2007.     

Weight function for a circular crack in the temperature problem of the theory of elasticity

A method for the construction of the weight function for a circular crack in an elastic body is proposed for problems of thermoelasticity. The case of an infinite body is studied in more detail. We deduce equations for the stress intensity factors in the cases where either temperature or the heat flow is specified on the crack surface and present some examples of their application. Kiev International University of Civil Aviation, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 91–98, November–December, 1998.     

Correlation of a plastic zone length near the tip of a mode I crack in an orthotropic material with anisotropy parameters

We derived equations that relate the length of a plastic zone near a mode I crack tip in a plate made of an orthotropic material with yield strength levels in the direction of the anisotropy axes. The case of crack orientation along one of the anisotropy axes is examined, with the latter being determined by the strain hardening of a material at the stage preceding the crack nucleation. The growth of yield strength along the axes lying in the plane of the plate is shown to result in smaller sizes of the plastic zone. An increase in yield strength in the direction of the normal to the above plane leads to an increase in its length. Ukrainian Regional Research and Design Institute of Civil Engineering, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 32–37, July–August, 1999.     

Influence of the modes of operation and structural factors on the crack propagation in 12Cr–2Ni–Mo steel

We study the influence of temperature, specimen sizes, loading frequency, and the time of holding under long-term static loading on the crack growth rate in 12Cr–2Ni–Mo steel. It is shown that the influence of these factors on the crack growth rate is insignificant. A numerical-experimental model is proposed for the evaluation of the time of subcritical crack growth with regard for the duration and cyclic character of loading. Translated from Problemy Prochnosti, No. 3, pp. 66–77, May–June, 2009.     

On a reliable equation for the second portion of the fatigue crack growth diagram

The fatigue crack growth kinetics on the second portion of the fatigue crack growth diagram is described using an equation that takes into account both the current crack tip opening displacement and the instant when the crack closure in a cycle vanishes and does not appear until the specimen failure. This instant corresponds to the critical effective SIF range, ΔK_fcl. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 83–87, May–June, 1999.     

Mechanics and physics of quasibrittle fracture of polycrystalline metals under conditions of stress concentration. Part 2. Theoretical basis

We propose a physical model of quasibrittle fracture of polycrystalline metals as applied to the most general case of the complex stressed state and nonuniform distributions of stress and strain fields. Within the framework of this model, on the basis of the analysis of elementary acts of the process of initiation and loss of stability of incipient cracks, we explain, for the first time, the basic regularities of the variation of the local stress of quasibrittle fracture σ_c, of a metal under the conditions of stress concentration. It is shown that the value of σ_c depends not only on the length of incipient cracks but also on their number in the local plastic zone at the notch tip and on the law of their distribution over orientations. On this basis, we explain the causes of the, influence of the acuity of the notch and testing temperature on σ_c. It is shown that the application of the proposed model in combination with the finite-element method makes it possible to predict (with sufficiently high accuracy) both the mean value and the spread of the fracture load of a specimen with stress concentrator of any acuity, including fatigue cracks. Institute of Physics of Metals, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 5–16, May–June, 1999.     

In-service fatigue fracture mechanisms in covered disks of a TV3-117VK helicopter turbine engine

In-service propagating fatigue cracks were examined in EI-698VD superalloy thin turbine covered disks of the first, second, and third stages of a TV3-117VK helicopter engine within service lifes of 200–1800 h. To reveal causes of early crack initiation and estimate a propagation time, metallographic and fractographic analyses were performed. The sequence of events during fatigue cracking of the disks was established. A block of striations on the fracture surface was discovered, which characterized fatigue crack propagation during one flight of a helicopter under different operating conditions. The number of striations in each block varied over the range of 4–20, being much more than those used to design covered disks. Fractographic results were used to estimate fatigue crack growth in covered disks of different stages using data on different operating conditions of helicopters. __________ Translated from Problemy Prochnosti, No. 1, pp. 171–174, January–February, 2008.     

Prediction of the service life of pipeline elements subjected to the action of hydrogen-containing media

We study the process of crack propagation in a preliminarily hydrogenated pipe placed in a hydrogen-containing medium. The crack growth rate is mainly controlled by the mass transport of hydrogen into the prefracture zone. We obtain an approximate solution of the problem of diffusion of hydrogen in the vicinity of the crack tip and establish the dependence of the crack growth rate on the crack tip opening displacement. This dependence is used for the determination of the residual service life of damaged elements of the pipe. The pipe is made of 4147 steel and the defect is modeled by a semielliptic longitudinal crack on the internal surface of the pipe. We show that the initial concentration of hydrogen may significantly accelerate the fracture process. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 4, pp. 43–48, July–August, 1999.     

MODEL-BASED STATISTICAL ANALYSIS OF SHORT FATIGUE CRACK GROWTH IN Ti 6Al-2Sn-4Zr-6Mo

Abstract— The framework of a new probabilistic model of short fatigue crack growth was laid down in the preceding paper. In this paper, the model is used to analyze growth rate statistics for surface fatigue cracks in Ti 6Al-2Sn-4Zr-6Mo. Specific models are proposed for the evolution of the stochastic growth control variable, which appears subsequently as an independent variable in a parametric law for the growth rate. Comparison with data shows that for cracks of length 10–250 μm in Ti 6–2-4–6, fluctuations in the instantaneous rate of propagation of each surface crack tip depend only on the visible surface microstructure in the tip's immediate neighborhood. They are not influenced by the microstructural environment of the subsurface crack front. Furthermore, they probably depend only on the sizes of at most the three grains nearest the crack tip, i.e. those within about 30 μm of it.     

BEHAVIOUR OF A 1Cr-1Mo-0.25V STEEL AFTER LONG-TERM EXPOSURE-II. CREEP CRACK INITIATION AND CREEP CRACK GROWTH

Both the initiation and the propagation of creep cracks have been studied in a 1Cr-1Mo-0.25V steel at 550°C using CT type specimens. The material taken from a large turbine casing was investigated in two conditions: (i) unaged and (ii) after a long exposure in-service time of about 150,000 h at 540°C. In both cases the material was found to be creep ductile, which is justified in terms of fracture mechanics applied to creeping solids. It is shown that fracture mechanics is unable to provide unique correlations with global load-geometry parameters, either K or C* for all the stages of both crack initiation and crack growth. However there exists a unique correlation between C* and the time to initiation, t_i. This correlation does not depend on the initial conditions of the material. During crack growth two stages are defined. Stage I is a transient regime in which C* is almost constant, but the correspondence between the crack growth rate and C* is not unique since largely dependent on the initial loading applied to the specimens. It is shown that the apparent correlation between the crack propagation rate in stage II which corresponds to large crack growth rate is doubtful. A simplified method based on reference length and reference stress is used to calculate C* parameter and to simulate the load-line displacement rate. The results obtained from this method are compared to those derived from finite element calculations published in the literature.