Elastic–plastic analysis of interaction between an interfacial crack and a subinterfacial microcrack in bi-materials

In the present work the finite element method is used to analyze the effect of interaction between an interfacial crack and a microcrack in ceramic/aluminum bi-materials. The behaviour is analyzed by the determination of the J integral, the plastic zone at the tips of the interfacial crack and the microcrack. The effects of longitudinal and transversal distance between the tips of the two cracks and the rotation of the microcrack are examined. The obtained results allow us to deduce a correlation between the position of the microcrack and the J integral and the plastic zone.The obtained results shows that the J integral at the interfacial crack tip reaches a maximum value when the microcrack is moved in the vicinity of the interfacial crack. With this distance the effect of interaction is marked more; the stress field at the microcrack tip and that of the interfacial crack generates only one plastic zone at the interfacial crack tip. The maximum size of the plastic zone is localised at the interfacial crack tip. Those of the two tips of the microcrack are very weak and even negligible in front of the zone plasticized at the interfacial crack tip.     

Influence of microcracking on crack-tip toughness of alumina

Al₂O₃-samples with different grain sizes were produced and the crack-tip toughness K_I0, also called intrinsic fracture toughness, was determined using two different measurement techniques. It appeared that K_I0 depends strongly on specimen grain size with the mechanistic link provided by the increase of microcrack density with grain size. Results obtained using measurements of crack opening displacements (COD) lie considerably lower than values based on a method using bending tests of pre-notched bend bars. It is suggested that the latter method relies on the use of a notch with a microcrack, which in fact is different than the behavior of a long crack alone.     

Molecular dynamics simulation of microcrack healing in copper

The molecular dynamics method is used to simulate microcrack healing during heating or/and under compressive stress. A center microcrack in Cu crystal could be sealed under a compressive stress or by heating. The role of compressive stress and heating in crack healing was additive. During microcrack healing, dislocation generation and motion occurred. If there were pre-existed dislocations around the microcrack, the critical temperature or compressive stress necessary for microcrack healing would decrease, and the higher the number of dislocations, the lower the critical temperature or compressive stress. The critical temperature necessary for microcrack healing depended upon the orientation of crack plane. For example, the critical temperature of the crack along (0 0 1) plane was the lowest, i.e., 770 K.     

Behavior of a tip of non-propagating fatigue crack during one stress cycle

Measurements and observations were made on the crack closure for the so-called non-propagating crack of notched specimens and for the non-propagating microcrack of unnotched specimens, which were formed in a rotating bending test of annealed carbon steel. Under the condition which produces the non-propagating crack, the ratio of stress range where the crack tip is open, to the full range of the cyclic stress tends gradually to zero with the increase in length of the crack initiated from a notch root.The tip of a non-propagating microcrack on the surface of a plain specimen is also recognized to be closed under the maximum stress level after 10⁷ cycles of the repetitions of the stress slightly below the fatigue limit.From these facts, it can be said that the tip of a so-called non-propagating crack or a non-propagating microcrack is hardly damaged by the repetition of stress which has produced each crack.     

A MICROCRACK GROWTH LAW FOR MULTIAXIAL FATIGUE

Within the past decade, critical plane approaches have gained increasing support based on correlation of experimentally observed fatigue lives and microcrack orientations under predominately low cycle fatigue (LCF) conditions for various stress states. In this paper, we further develop an engineering model for microcrack propagation consistent with critical plane concepts for correlation of both LCF and high cycle fatigue (HCF) behavior, including multiple regimes of small crack growth. The critical plane microcrack propagation approach of McDowell and Berard serves as a starting point to incorporate multiple regimes of crack nucleation, shear growth under the influence of microstructural barriers, and transition to linear crack length-dependent growth related to elastic-plastic fracture mechanics (EPFM) concepts. Microcrack iso-length data from uniaxial and torsional fatigue tests of 1045 steel and IN 718 are examined and correlated by introducing a transition crack length which governs the shift from nonlinear to linear crack length dependence of da/dN. This transition is related to the shift from strong microstructural influence to weak influence on the propagation of microcracks. Simple forms are introduced for both the transition crack length and the crack length-dependence of crack growth rate within the microcrack propagation framework (introduced previously by McDowell and Berard) and are employed to fit the 1045 steel and IN 718 microcrack iso-length data, assuming preexisting sub-grain size cracks. The nonlinear evolution of crack length with normalized cycles is then predicted over a range of stress amplitudes in uniaxial and torsional fatigue. The microcrack growth law is shown to have potential to correlate microcrack propagation behavior as well as damage accumulation for HCF-LCF loading sequences and sequences of applied stress states.     

A mathematical equation relating low cycle fatigue data to fatigue crack propagation rates

A mathematical equation is derived to predict fatigue crack growth rates on the basis of a J integral analysis from the fatigue fracture behaviour of low cycle fatigue samples. According to this equation, the fatigue crack propagation curves can be predicted if low cycle fatigue data and an initial microcrack size are available. The results obtained from this study show that the predicted fatigue crack propagation rates for Ti-24V, Ti-6Al-4V and Al-6Zn-2Mg alloys are very close to experimental values.     

频繁启停过程中拉杆微裂纹引起的组合转子性能退化研究

燃气轮机的性能下降很大程度上是由于燃机的核心部件——组合转子的退化导致的,因此,非常有必要重点研究组合转子的性能退化规律.组合转子局部结构的损伤,必将导致整体性能的下降.从该角度出发,建立组合转子的有限元模型,对组合转子拉杆裂纹进行扩展计算,定义组合转子性能退化量,分析了不同尺寸的拉杆裂纹对转子性能退化的影响.研究结果表明:随着裂纹尺寸的逐渐增加,组合转子的退化速率逐渐加快;不同微裂纹拉杆的分布形式对组合转子退化程度影响不同,当微裂纹拉杆相邻分布时组合转子退化速率最快,裂纹拉杆180°分布时组合转子退化速率最慢.     

Influence of microcracking and homogeneity on the mechanical behaviour of (Al2O3 + ZrO2) ceramics

Quantitative methods for estimations of microcrack density and dispersion homogeneity give evidence of microcrack generation on macrofracture as the dominating mechanism responsible for toughening. The efficiency of energy dissipation at one microcrack density is higher in zirconia-toughened alumina than in pure Al₂O₃ ceramics. Deterioration of dispersion homogeneity results in the promotion of subcritical crack growth and low strength due to large flaw sizes at instability.     

Structural-simulation modeling of the fritting and fracture of a ferroelectric ceramic

Results are presented from a structural-simulation modeling of the processes that occur during the fritting and fracture of ferroelectric ceramics BaTiO₃ and PbTiO₃. A study was made of anomalous grain growth and the effect of these grains on the spontaneous cracking of the materials. Also examined are features of the propagation of a macrocrack in the modeled structure with allowance for the microcrack region formed in the neighborhood of the crack tip. Alternative microcrack patterns that lead to a change in the strength of the material are discovered, and estimates are obtained for different strength characteristics: crack density; the dimensions of the prefracture region; the crack resistance of the ceramic; local strengthening and shielding of the macrocrack by the microcrack region at its tip.Translated from Problemy Prochnosti, No. 8, pp. 77–86, August, 1994.     

Stochastic microcrack nucleation in lamellar solids

Growth of a crack across an interface between two grains of an elastic lamellar material having different lamellar orientations is investigated for materials having a heterogeneous spectrum of individual lamellar toughnesses. Numerical analyses carried out using a cohesive zone model and the finite element method show that microcracking in the adjacent lamellae can preferentially occur at low-toughness lamellae spatially remote from the crack tip rather than at higher-toughness lamellae close to the crack tip. An analytic model based on linear elastic fracture mechanics and an initial microcrack is shown to predict the location and macroscopic toughness at which microcrack nucleation and growth occur in good agreement with the numerical analyses, using only the initial microcrack size as a single parameter. These results demonstrate that microcrack nucleation requires a sufficiently high stress over a sufficiently large region and thus that microcrack nucleation ahead of a main crack can be the dominant small-scale damage mechanism in such heterogeneous systems.     

Effect of microcrack array on stress intensity factor of main crack

An improved technique for solving crack-microcrack interaction problems is developed, based on the Green's function for a dislocation dipole placed in the vicinity of a main crack. The microcrack array is characterized by the microcrack density, orientation and length distributions. The stress field near the main crack tip is taken as a sum of a singular term of an anisotropic problem with stress intensity factor K, and a regular term. K and the regular term are determined from a system of equations obtained by self-consistency arguments. The proposed technique is illustrated by numerical solutions of several interaction problems for particular configurations of microcrack array.     

Interaction effect crack–interfacial crack using finite element method

The interaction effect of an interfacial crack–microcrack modifies considerably the fracture behaviour of S45C/Si₃N₄ bimaterial. This work aims at studying the interaction effect of a crack located in one of the materials constituting the assembly near the interface, and that between an interfacial crack and a microcrack parallel to the interface by using the finite element method. The effect of transverse and longitudinal interaction distances between the interfacial crack and the microcrack are highlighted. The stress intensity factor of the interacting cracks and the bimaterial mechanical properties influence on the conditions of deviation and propagation of crack by interface and intercrack are examined.     

Propagation of microcracks at stress amplitudes below the conventional fatigue limit in Ti–6Al–4V

Fatigue crack growth below the conventional fatigue limit was examined in Ti–6Al–4V in two different microstructural conditions, bi-modal and fully lamellar. Tests conducted at R = −1, at room temperature and in air showed that there is a stress dependency in the d a /d N –Δ K behaviour in both microstructures. The increasing crack front roughness associated with increasing crack size results in a decrease in the crack growth rate relative to the crack growth rate in a single grain. The d a /d N vs. Δ K lines were drawn for each crack size and a 'threshold'Δ K was determined using the intercept of the lines with d a /d N = 10⁻¹⁰ m cycle⁻¹. These values were used to construct modified Takahashi–Kitagawa diagrams to predict microcrack growth below the fatigue limit for each microstructure. A comparison of the two microstructures indicated differences in behaviour in microcrack and macrocrack growth that were explained by differences in crack front roughness at a given crack size.     

Critical linkages of coalescing microcracks under stress loading

ABSTRACT The fracture process of brittle materials with randomly orientated microcracks critically depends on strong interactions among microcracks and the coalescence path that leads to a fatal crack. In this paper, a model based on the coalescence process for planar orientated microcracks is presented. An energy ratio is defined as the competition between the potential energy release and the new crack surface energy in each coalescence step, which is a token of the excessive driving force for microcrack propagation. A critical linkage dictates the coalescence of microcracks under stress loading. Probabilities of microcrack coalescence dominated by the first linkage and subsequent linkages are analysed for collinear and wavy microcrack arrays in detail.     

A fracture mechanics model for the analysis of micro-pitting in regard to lubricated rolling–sliding contact problems

A computational model is presented for the analysis of micro-pitting in regard to lubricated rolling–sliding contact problems. This model assumes the appearance of an initial microcrack on the contact surface due to the mechanical or thermal treatment of the material, and as a consequence of an on-going process in early the stage of exploitation. The discretised model of the contacting mechanical elements is subjected to normal loading (Hertzian contact pressure), tangential loading (friction between contacting surfaces) and internal pressure to the crack surfaces. Crack propagation is predicted as follows: (1) using modified maximum tangential stress criterion, which takes into account the influence of stress intensity factors K_I and K_II, T-stress, stress on the crack’s surface caused by lubricant pressure inside the crack, and the critical distance ahead of the crack tip and (2) the classical maximum tangential stress criterion, which only takes into account the influence of the stress intensity factors K_I and K_II. The stress intensity factor based on these two criteria is then used in a short crack growth theory to determine the fatigue life of an initial crack to extent up to micro-pit. The developed model is applied to a real spur gear pair.     

Microcrack growth and fatigue behavior of a duplex stainless steel

The kinetics of microcrack growth during cycling has been studied in a S32205 duplex stainless steel in the as-received and aged (100 h at 475 °C) conditions. Cylindrical specimens with a shallow notch were subjected to a constant plastic strain range of 0.3% in both thermal conditions. The characteristic features of surface damage and crack growth showed striking differences in microcrack density, nucleation location and propagation rate between the two thermal conditions even though the fatigue lives are comparable. In the as-received material, microcrack density is low and they nucleate mainly at grain and phase boundaries or second-phase particles. In the aged condition, slip markings first appear in the ferritic phase and they are the preferred site for microcrack nucleation. Crack propagation takes place along slip markings in adjacent grains for crack lengths less than 100 μm. A comparison between fatigue life and the relevant parameters of a microcrack growth law was made.     

Stress field interaction and strain energy distribution between a stationary main crack and its process zone

The damage process zone developed by brittle materials in front of a macrocrack is simulated by means of a distribution of microcracks. Crack mutual interactions are taken into account by means of a numerical technique, based on a displacement discontinuity boundary element method that is able of considering both the macrocrack–microcrack and microcrack–microcrack interactions inside the process zone. In the frame of linear elastic fracture mechanics the stress field at each crack tip and the related elastic strain energy are calculated. The main features of the interaction phenomena turn out to be almost independent of the microcrack density. Some considerations both on the shielding and amplification effects on the main crack and on the strain energy distribution between cracks give explanation to experimental evidence and prove that crack interaction is not such a short-range effect as sometimes expected.     

Interaction of a penny-shaped crack with an elliptic crack

Three-dimensional problem of crack-microcrack interaction is solved. Both the crack and microcrack are embedded in an infinite isotropic elastic medium which is subjected to constant normal tension at infinity. One of the cracks is circular while the other is elliptic and they are coplanar and are positioned in such a way that the axis of the elliptic crack passes through the centre of the circular crack. A recently developed integral equation method has been used to solve the corresponding two dimensional simultaneous dual integral equation involving the displacement discontinuity across the crack faces that arises in such an interaction problem. A series of transformations first reduce them to a quadruplet infinite system of equations. A series solution is finally obtained in terms of crack separation parameter which depends on the separation of the crack microcrack centre. Analytical expression for the stress intensity factors have been obtained up to the order ⁶. Numerical values of the interaction effect have been computed for and results show that interaction effects fluctuate from shielding to amplification depending on the location of each crack with respect to the other and crack tip spacing as well as the aspect ratio of the elliptic crack. The short range interaction can play a dominant role in the prediction of crack microcrack propagation.     

Microcrack propagation and fatigue lifetime under non-proportional multiaxial cyclic loading

Non-proportional multiaxial fatigue tests of tubular specimens were performed under purely alternating strain-controlled loading. Different loading paths with different phase shifts were applied. With increasing phase shift at the same equivalent load, the lifetime was found to increase. For lifetime prediction a model based on the Manson–Coffin law was developed. By including the hydrostatic loading part, it was possible to compare the results of the multiaxial fatigue tests with uniaxially ascertained results. To obtain more information about the microcrack behaviour under multiaxial non-proportional loading, sonic emission studies and fractographic analyses were performed. The results suggest a discontinuous microcrack propagation. Motivated by the good agreement between these observations and some microcrack propagation models known from literature, a simplified model was proposed for micro and short crack propagation. This model which is based on the J-integral range ΔJ yields a quite good agreement between the experimentally observed and the calculated lifetimes.     

Simulation des Mikrorisswachstums unter Schwingbeanspruchung. Teil 1: Modell und Simulationsergebnisse,Mikrorisswachstum, Streuung,Einfluss von Beanspruchungsart und ‐höhe,Risskeimdichte und Korngröße

Simulation of fatigue microcrack growth. Part 1: Modelling and results of simulation, microcrack growth, scatter, effect of load condition, density of microcrack seeds and grain size Presented is a simulation of microcrack growth under alternating stresses. Microstructural barriers and the state of stress play a dominant role in the early stages of crack growth of metals. The polycristalline metal was modeled as an aggregat of hexagonal grains with a different crystallographic orientation of each grain. The effect of grain bounderies on stage I crack growth is considered in the model. The mode of shear crack growth is analyzed on the basis of microstructural crack growth within the first few grains, where the crack growth decelerates as the crack tip gets closer to the grain boundery. Normal stress crack growth has been considered for those cracks which are longer than microstructurelly short cracks, so‐called physically small cracks. Furthermore the transition from stage I to stage II growth is considered. The model is applied for thinwalled tubular specimens of the ferritic steel AlSI 1015 and the aluminium alloy Al Mg Si 1 subjected to tension and torsion as well as combined tension‐torsion loading. Also different load sequences are investigated. The microstructural crack pattern and crack distribution can sucessfully simulated with the model. The crack growth behaviour and the effect of lifetime until a crack length of 500 μm ist presented for numerous parameters.