Matrix cracking in crossply ceramic matrix composites under quasi-static and cyclic loading

Experimental data are presented for the development of 90° ply and 0° ply cracking in two crossply silicon carbide fibre/calcium aluminosilicate matrix laminates under quasi-static loading. under mechanical fatigue loading it is found that there is an increase in ply crack densities and a corresponding laminate stiffness reduction with cycling. Possible mechanisms to account for these observations are proposed. A model is presented which describes the stress/strain behaviour as a function of crack densities based on assumptions of frictional load transfer between fibre and matrix in the longitudinal plies and elastic bonding between the longitudinal and transverse plies.     

Fatigue Fracture of Concrete Subjected to Biaxial Stresses in the Tensile C–T Region

In this paper cyclic quasi-static and constant amplitude fatigue responses of concrete subjected tensile compression–tension (C–T) biaxial stress are presented. In the tensile C–T region within the biaxial stress space, magnitude of the principal tensile stress is larger than or equal to that of the principal compressive stress. An experimental program consisted of subjecting hollow, cylindrical concrete specimens to torsional loading. Failure in both quasi-static and fatigue is due to crack propagation. It is shown that the crack propagation resulting from the biaxial loading can be predicted using Mode I fracture parameters. The fatigue crack growth is observed to be a two-phase process: an acceleration stage that follows a deceleration stage. The crack length where the rate of crack growth changes from deceleration to acceleration is shown to be equal to the crack length at the quasi-static peak load. Analytical expressions for crack growth in the deceleration and acceleration stages are developed in terms of the mechanisms that influence quasi-static crack growth. The model parameters obtained from uniaxial fatigue tests are shown to be sufficient for predicting the biaxial fatigue response. Finally, a fracture-based fatigue-failure criterion is proposed, wherein the fatigue failure can be predicted using the critical Mode I stress intensity factor.     

Crack Propagation in Flexural Fatigue of Concrete

In this paper the behavior of concrete subjected to flexural fatigue loading is studied. Notched concrete beams were tested in a three-point bending configuration. Specimens were subjected to quasi-static cyclic and constant amplitude fatigue loading. The cyclic tests were performed by unloading the specimen at different points in the postpeak part of the quasi-static loading response. Low cycle, high amplitude fatigue tests were performed to failure using four different load ranges. The crack mouth opening displacement was continuously monitored throughout the loading process. Crack propagation caused by quasi-static and fatigue loads is described in terms of fracture mechanics. It is shown that the crack propagation in the postpeak part of the quasi-static load response is predicted using the critical value of the mode I stress intensity factor (KIC). The ultimate deformation of the specimen during the fatigue test is compared with that from the quasi-static test; it is demonstrated that the quasi-static deformation is insufficient as a fatigue failure criterion. It is observed that crack growth owing to constant-amplitude fatigue loading comprises two phases: a deceleration stage when there is a decrease in crack growth rate with increasing crack length, followed by an acceleration stage where the rate of crack growth increases at a steady rate. The crack length where the rate of crack growth changes from deceleration to acceleration is shown to be equal to the crack length at the peak load of the quasi-static response. Analytical expressions for crack growth in the deceleration and acceleration stages are developed, wherein the expressions for crack growth rate in the deceleration stage are developed using the R-curve concept, and the acceleration stage is shown to follow the Paris law. It is observed that the crack length at failure for constant amplitude fatigue loading is comparable to that of the corresponding load in the postpeak part of the quasi-static response. Finally, a fracture-based fatigue failure criterion is proposed.     

Fatigue oxidation interaction in a superalloy—application to life prediction in high temperature low cycle fatigue

A study of the interaction between fatigue and oxidation has been carried out in the case of a cast cobalt base superalloy MARM 509 tested in laboratory air at 900 °C. The influence of fatigue cycling on oxidation of this alloy has been studied by quantitative metallography on polished specimens exposed to air in a furnace and on strain-cycled low-cycle fatigue specimens. The oxidation kinetics were determined by thickness measurements for matrix oxidation and by oxidized depth measurements for the preferential oxidation of MC carbides. In both cases the oxidation kinetics were found to be dramatically enhanced by cycling for the matrix oxidation according to a linear relationship with plastic strain amplitude and less dramatically for carbides according to an exponential relationship with the maximum cyclic stress. From these observations a damage equation which describes fatigue damage as a crack growth process has been proposed: the elementary crack advance is a summation of a mechanical contribution due to the fatigue process itself which is described by Tomkins’ equation and of an oxidation contribution which has been evaluated from metallographic measurements. Integration of this crack growth equation gives predicted fatigue lives which are in good agreement with experimental results within a factor of two.     

Production of an Aluminium-Rich Magnesium Silicide Alloy from Atomized Powder

Abstract

Two material models are developed to estimate the effect of density on the static and cyclic fracture behaviour of a sintered steel. The models are based on the known micromechanisms of failure for each type of loading. Theoretical predictions are compared with previous experimental results taken from a companion paper (preceding). The two models successfully account for the variation of yield stress, ultimate tensile stress, and fracture toughness with density. They prove less successful in predicting the effect of density on fatigue crack propagation behaviour. PM/0198     

Subcritical fatigue crack growth in alumina—II. Crack bridging and cyclic fatigue mechanisms

A crack re-notching procedure based on the “hinged straight crack” approximation is used to determine the distribution and magnitude of the bridging traction, σ(X), existing over the faces of the fatigue cracks grown in the experiments of Part I. From this distribution, the σ(u) relation between the bridging tractions and the crack opening is obtained and a simple method is tentatively proposed to measure the magnitude of the crack bridging stress intensity factor, K_b. The characteristics of the σ(X) and σ (u) relations are discussed in the light of the microscopical observations of crack profiles and in terms of the distribution of the frictional and elastic ligaments existing along the faces of the cracks. Crack growth rates and behaviour under different values of stress ratio R are compared and mechanisms of fatigue crack growth vs static crack growth are proposed.     

Kinetics of environmental fatigue crack growth in a nickel-copper alloy: Part II. In hydrogen

A systematic matrix of fatigue crack growth rate data in a hydrogen environment has been generated in a nickel-copper alloy and compared with the base line data in the milder oxygen and vacuum environments described in the preceding paper. It is found that crack growth in the hydrogen environment is characterized by high values of the Paris equation exponent and faster crack propagation rates as compared to those in the milder environments. Fractographic examination shows that brittle inter granular separation occurs superimposed on an otherwise ductile crack mode in the hydrogen tests. Quantitative fractographic analysis of the hydrogen affected fracture surfaces indicates that the percentage of intergranular failure (area fraction) is a uniquely related function of the mean stress intensity rather than the maximum stress intensity level of fatigue loading. This dependence is discussed in terms of dislocation sweep-in transport of hydrogen deep into the plastic zone during fatigue cycling. Formerly a Graduate Student at Columbia University Formerly Senior Staff Associate, Science Center, Rockwell International     

Multiple matrix cracking in a fiber-reinforced titanium matrix composite under high-cycle fatigue

An experimental study of multiple matrix cracking in a fiber-reinforced titanium alloy has been conducted. The focus has been on the effects of stress amplitude on the saturation crack density and the effects of crack density on hysteresis behavior. Comparisons have been made with predictions based on unit cell models, assuming the sliding resistance of the interface to be characterized by a constant interfacial shear stress. In addition, independent measurements of the sliding stress have been made using fiber pushout tests on both pristine and fatigued specimens. D.P. WALLS, Graduate Student, formerly with the Materials Department, University of California, Santa Barbara     

Influence of hold times on the low cycle fatigue behaviour of the material in 792

The LCF- (low cycle fatigue) tests performed on the alloy IN 792 showed the influence of temperature and the tension hold time which is already known from ferritic steels. An additional effect of the compression hold time was found. A shift of the hysteresis loop in the tension range during tests including compression hold times takes place. Thus the effective mean stress is also in the tensile range and as a consequence influences crack initiation and propagation. A significant reduction of fatigue endurance in tests with compression hold times compared with pure tension hold time tests could be observed. This specific behaviour of Ni-based alloys could be explained on the basis of a different cyclic hardening/softening behaviour or relaxation behaviour within the tension and compression range. In contrast to this, however, the effect of compression hold times can be described by means of the Smith-Watson-Topper parameter.     

Analyses of Pressure Requirements for Powder Compact Extrusions

Abstract

The tensile strength, fatigue crack propagation behaviour, and fracture toughness of a low-alloy sin tered steel were determined for the porosity range 11–17%. Static and cyclic strength were found to increase with density in a non-linear fashion. The pores both exerted a stress-concentrating influence and reduced the load-bearing section. The micromechanism of failure was always ductile fracture in the necks between sintered steel particles. It was concluded that the stress state at the tips of cracks subjected to static or cyclic loading was closer to plane stress than to plane strain. Retardation of fatigue crack propagation appeared to occur due to the blunting action of the pores. The presence of a wear mechanism had little influence upon fatigue crack growth rates. A companion paper (following) attempts to model the static and cyclic behaviour of the steel, based on the known micromechanisms of failure. PM/0172     

The mechanics of matrix cracking in brittle-matrix fiber composites

Matrix fracture in brittle-matrix fiber composites is analyzed for composites that exhibit multiple matrix cracking prior to fiber failure and have purely frictional bonding between the fibers and matrix. The stress for matrix cracking is evaluated using a stress intensity approach, in which the influence of the fibers that bridge the matrix crack is represented by closure tractions at the crack surfaces. Long and short cracks are distinguished. Long cracks approach a steady-state configuration, for which the stress intensity analysis and a previous energy balance analysis are shown to predict identical dependence of matrix cracking stress on material properties. A numerical solution and an approximate analytical solution are obtained for smaller cracks and used to estimate the range of crack sizes over which the steady-state solution applies.     

Effect of SiC volume fraction and particle size on the fatigue resistance of a 2080 Al/SiC p composite

The effect of SiC volume fraction and particle size on the fatigue behavior of 2080 Al was investigated. Matrix microstructure in the composite and the unreinforced alloy was held relatively constant by the introduction of a deformation stage prior to aging. It was found that increasing volume fraction and decreasing particle size resulted in an increase in fatigue resistance. Mechanisms responsible for this behavior are described in terms of load transfer from the matrix to the high stiffness reinforcement, increasing obstacles for dislocation motion in the form of S’ precipitates, and the decrease in strain localization with decreasing reinforcement interparticle spacing as a result of reduced particle size. Microplasticity was also observed in the composite, in the form of stress-strain hysteresis loops, and is related to stress concentrations at the poles of the reinforcement. Finally, intermetallic inclusions in the matrix acted as fatigue crack initiation sites. The effect of inclusion size and location on fatigue life of the composites is discussed.     

Frequency dependent low cycle fatigue crack propagation

The frequency modified Coffin-Manson low cycle fatigue expression phenomenologically describes the influence of the cycling frequency on the fatigue life. This expression relates only to the fatigue life and as such does not enable the separation of the frequency influence on crack nucleation from that on propagation. The approach taken here was to study directly the propagation phase of low cycle fatigue and to this end a frequency modified crack growth expression is presented. The experiments reported here were performed on A286 (an iron-base superalloy) cycled at 1100°F with plastic strain limits. The influence of the cycling frequency is described in terms of two frequency regimes. At the lowest frequencies (below 0.05 cpm) varying the frequency did not change the time to failure. The crack growth rate is thus more a result of stress rupture than fatigue. At higher frequencies both time and cycles determine the crack propagation behavior.     

The Significance of Crack Initiation Stage in Very High Cycle Fatigue of Steels

Different stages of the Very High Cycle Fatigue (VHCF) crack evolution in tool steels have been explored using a 20 kHz ultrasonic fatigue testing equipment. Extensive experimental data is presented describing VHCF behaviour, strength and crack initiating defects in an AISI H11 tool steel. Striation measurements are used to estimate fatigue crack growth rate, between 10^?8 and 10^?6 m/cycle, and the number of load cycles required for a crack to grow to critical dimensions. The growth of small fatigue cracks within the “fish‐eye” is shown to be distinctively different from the crack propagation behaviour of larger cracks. More importantly, the crack initiation stage is shown to determine the total fatigue life, which emphasizes the inherent difficulty to detect VHCF cracks prior to failure. Several mechanisms for initiation and early crack growth are possible. Some of them are discussed here: crack development by local accumulation of fatigue damage at the inclusion – matrix interface, hydrogen assisted crack growth and crack initiation by decohesion of carbides from the matrix.     

Fatigue crack growth of SM-1240/TIMETAL-21S metal matrix composites at elevated temperatures

A series of high-temperature fatigue crack growth experiments was conducted on a continuous-fiberreinforced SM1240/TIMETAL-21S composite using three different temperatures, room temperature (24 °C), 500 °C, and 650 °C, and three loading frequencies, 10, 0.1, and 0.02 Hz. In all the tests, the cracking process concentrated along a single mode I crack for which the principal damage mechanism was crack bridging and fiber/matrix debonding. The matrix transgranular fracture mode was not significantly influenced by temperature or loading frequency. The fiber debonding length in the crack bridging region was estimated based on the knowledge of the fiber pullout lengths measured along the fracture surfaces of the test specimens. The average pullout length was correlated with both temperature and loading frequency. Furthermore, the increase in the temperature was found to lead to a decrease in the crack growth rate. The mechanism responsible for this behavior is discussed in relation to the interaction of a number of temperature-dependent factors acting along the bridged fiber/matrix debonded zone. These factors include the frictional stress, the radial stress, and the debonding length of the fiber/matrix interface. In addition, the crack growth speed was found to depend proportionally on the loading frequency. This relationship, particularly at low frequencies, is interpreted in terms of the development of a crack tip closure induced by the relaxation of the compressive residual stresses developed in the matrix phase in regions ahead of the crack tip during the time-dependent loading process.     

Transient creep in mild steel and copper at room temperature

Transient creep curves were obtained from mild steel and copper specimens which had been work hardened by cycling. Results are presented in terms of an “overstress” model in which strain rates are related to differences between the actual stress and the corresponding stress-strain point on a quasi-static stress-strain curve. It is further shown that a semi-empirical equation used to describe steady state plastic deformation can be adapted to describe transient behaviour when re-written in terms of the ‘overstress’ rather than the actual stress.     

Application of minimum energy formalism in a multiple slip band model for fatigue—II. Crack nucleation and derivation of a generalised Coffin-Manson law

A situation of multiple parallel slip bands is considered. Each slip band is modelled as an accumulation of edge dipoles. The dislocation dipole density within the slip bands continually increases with fatigue cycling. The strain energy density within the slip bands consequently builds up with cycling until a critical cycle number when it becomes energetically favorable to nucleate a microcrack within one of the slip bands. This is proposed to be the crack nucleation cycle number. The above criterion based on the strain energy density is used to derive an explicit expression for the number of cycles for crack nucleation. It is shown that there is a parallel between this criterion for crack nucleation and other criteria that are based on the accumulation of a certain critical amount of damage. A generalised Coffin-Manson law for crack initiation is also derived. The size and most likely site of the just-nucleated crack is discussed.     

Mode I fatigue cracking in a fiber reinforced metal matrix composite

The mode I fatigue crack growth behavior of a fiber reinforced metal matrix composite with weak interfaces is examined. In the longitudinal orientation, matrix cracks initially grow with minimal fiber failure. The tractions exerted by the intact fibers shield the crack tip from the applied stress and reduce the rate of crack growth relative to that in the unreinforced matrix alloy. In some instances, further growth is accompanied by fiber failure and a concomitant loss in crack tip shielding. The measurements are compared with model predictions, incorporating the intrinsic fatigue properties of the matrix and the shielding contributions derived from the intact fibers. The magnitude of the interface sliding stress inferred from the comparisons between experiment and theory is found to be in broad agreement with values measured using alternate techniques. The results also indicate that the interface sliding stress degrades with cyclic sliding, an effect yet to be incorporated in the model. In contrast, the transverse fatigue properties are found to be inferior to those of the monolithic matrix alloy, a consequence of the poor fatigue resistance of the fiber/matrix interface.     

基于有限元方法的疲劳裂纹闭合行为

裂纹闭合行为将很大程度改变疲劳裂纹扩展行为。针对316L不锈钢,结合常幅加载和单个拉伸过载试验和动态数值模拟方法,对疲劳裂纹扩展行为中的裂纹闭合现象开展了一系列研究工作。详细对比了不同扩展阶段的裂纹闭合行为随裂纹长度、应力比和过载影响因素的变化,以及对裂纹扩展速率的影响。同时,研究了单个拉伸过载和裂纹闭合行为之间的内在联系和机理。结合裂纹闭合理论和有限元计算结果,等效应力强度因子被用来描述316L不锈钢的裂纹扩展过程,并提出316L不锈钢的裂纹扩展速率的预测模型。     

Effects of sic content on fatigue crack growth in

An experimental study has been conducted with the purpose of examining the fatigue crack growth characteristics of cast aluminum alloy matrix composites reinforced with different vol- ume fractions of silicon carbide particles. Particular attention has been paid to developing com- posite microstructures with similar matrix aging condition, precipitation, matrix strength, reinforcement particle size distribution, and interfacial characteristics but with different con- trolled amounts of reinforcement particles. Fatigue crack growth experiments have been con- ducted using constant stress amplitude methods with a fixed load ratio as well as constant K_max control involving a varying load ratio. The development of crack closure and the microscopic path of the crack through the composite microstructure are monitored optically and using the electron microscope in an attempt to examine the mechanisms of fatigue fracture. The results indicate that an increase in SiC content results in the suppression of striation formation in the ductile matrix. Although ductile matrix failure involving the formation of striations in the low SiC content composite or of void growth in the high SiC content composite is evident, the results also show that fracture of the reinforcement particles plays a significant role in dictating the rates of fatigue crack growth. Detailed quantitative analyses of the extent of particle fracture as a function of the reinforcement content have been performed to elucidate the mechanistic origins of fatigue resistance. The propensity of particle fracture increases with particle size and with the imposed value of stress intensity factor range. While discontinuously reinforced metal- matrix composites with predominantly matrix cracking are known to exhibit superior fatigue crack growth resistance as compared to the unreinforced matrix alloy, the tendency for particle fracture in the present set of experiments appears to engender fatigue fracture characteristics in the composite which are inferior to those seen in the unreinforced matrix material. Particle fracture also results in noticeable differences in the microscopic fracture path and causes a reduction in crack closure in the composites as compared to that in the matrix alloy. The results of this work are discussed in light of other related studies available in the literature in an attempt to develop a mechanistic perspective on fatigue crack growth resistance in metal-matrix composites.