H. Ghonem

Some issues in the application of cohesive zone models for metal–ceramic interfaces

Abstract Cohesive zone models (CZMs) are being increasingly used to simulate discrete fracture processes in a number of homogeneous and inhomogeneous material systems. The models are typically expressed as a function of normal and tangential tractions in terms of separation distances. The forms of the functions and parameters vary from model to model. In this work, two different forms of CZMs (exponential and bilinear) are used to evaluate the response of interfaces in titanium matrix composites reinforced by silicon carbide (SCS-6) fibers. The computational results are then compared to thin slice push-out experimental data. It is observed that the bilinear CZM reproduces the macroscopic mechanical response and the failure process while the exponential form fails to do so. From the numerical simulations, the parameters that describe the bilinear CZM are determined. The sensitivity of the various cohesive zone parameters in predicting the overall interfacial mechanical response (as observed in the thin-slice push out test) is carefully examined. Many researchers have suggested that two independent parameters (the cohesive energy, and either of the cohesive strength or the separation displacement) are sufficient to model cohesive zones implying that the form ( shape ) of the traction–separation equations is unimportant. However, it is shown in this work that in addition to the two independent parameters, the form of the traction–separation equations for CZMs plays a very critical role in determining the macroscopic mechanical response of the composite system.

Intergranular crack tip oxidation mechanism in a nickel-based superalloy

Abstract This paper is concerned with the intergranular crack tip oxidation mechanism in alloy 718 at elevated temperatures. The basic concept is based on the ability of the oxygen partial pressure to control the preferential formation of oxide layers at the crack tip. The time required to complete the build-up of the protective oxide type at the metal-oxide interface is considered a measure of the limits of the oxidation process. Identification by transmission electron microscopy of oxide scale formed along fracture surfaces during a low frequency fatigue crack process in alloy 718 at 650°C supports the proposed model concepts. An experimental program was carried out to investigate the role of passivation time in controlling the progressive process of crack tip oxidation. This was achieved by testing the influence of oxide buil-up during hold time at minimum load, as well as the effect of a minor high frequency cycle imposed on the hold time period. It was established that an increase in fatigue crack growth rate accompanies the increase in passivation time period. These results were interpreted on the basis of the oxidation formation concepts.

Interfacial mechanics of push-out tests : theory and experiments

Abstract The thermo-mechanical characterization of interfaces in composite systems (PMC/MMC/IMC/CMC) is one of the challenging problems in composite mechanics and engineering. Each system has its own distinguishing features; however, in MMCs and IMCs the study is rendered more complex due to the evolving chemical species (both temporally and spatially), and the multi-axial state of residual stresses. Before MMCs or IMCs can be used in actual applications, the role of interfaces in not only the strengthening but also toughening mechanisms needs to be clearly understood. For evaluating the interfacial mechanical properties of interfaces, thin slice push-out test has emerged as the de-facto standard. Though, conceptually the testing procedure is simple, interpretation of the test results is not. It is essential to conduct very careful experiments, make precise meso- and macroscopic chemical/structural/mechanical observations and perform a thorough theoretical/numerical simulation before the test data can be used in a quantitative manner. In this paper, a comprehensive analysis of the push-out test is presented based on the theoretical/numerical and experimental research work of the authors’ group during the past few years. In this work, thin slice push-out tests were conducted primarily on Titanium Matrix Composites at various test temperatures (room and elevated) with different processing conditions (temperature and time). Different composite systems with Titanium based matrices (Ti–6Al–4V, Timetal 21S, Ti–15Nb–3Al) uniaxially reinforced with Silicon Carbide fibers (SCS-6) were chosen for the study. Effect of the evolution of interfacial chemistry and architecture (in matrix, coating and reaction zone) on both shear strength τ s and frictional strength τ f were studied. A novel finite element analysis based on nonlinear finite element method was implemented, in which not only the initiation but propagation of interfacial cracks are simulated. In the analysis, both shear stress and fracture energy based criteria are used to model the initiation of (closed) cracks. Quantitative values of τ s , τ f , G I and G II are then extracted based on the experimental data and the numerical simulation. A critical review of stress and energy based interface-modeling approaches and their applicability to various boundary value problems are made.

Experimental study of the constant-probability crack growth curves under constant amplitude loading

Abstract This paper is concerned with the application of a mathematical model that describes the fatigue crack growth evolution and associated scatter in polycrystalline solids. The model has been built on the basis that an analogy exists between a particular discontinuous Markovian stochastic process, namely the general pure birth process, and the crack propagation process. The, crack evolution and scatter were then defined in terms of material, stress and crack-length dependent properties and crack tip incubation time. The application of the model is carried out by comparing the constant-probability crack growth curves generated for three different load levels with those obtained from testing sixty A1 7075-T6 specimens for each load level. A photographic method was utilized to measure the cracklength in this test program, by recording the residual deformation that accompanies the flanks of the crack during propagation.

Depth of intergranular oxygen diffusion during environment-dependent fatigue crack growth in alloy 718

The elevated-temperture fatigue crack growth behavior in alloy 718, when subjected to a loading frequency lower than the transitional frequency of this alloy, is viewed as fully environment dependent. In this process, the crack growth increment per loading cycle is assumed to be equal to the intergranular oxygen diffusion depth at the crack tip during the cycle effective oxidation time. In order to identify the trend of this diffusion depth an experimental program was carried out on compact tension specimens made of alloy 718 at 650 °C in which fatigue crack growth measurements were made for cyclic load conditions with and without hold time periods at minimum load level. This work resulted in establishing a relationship correlating the intergranular oxygen diffusion depth and the value of the stress intensity factor range ΔK. This relationship, when integrated over the cycle effective oxidation time, results in a closed-form solution describing the environment-dependent fatigue crack growth rate. A comparison is made between the results of this solution when applied to different loading frequencies and the corresponding experimental results. This comparison shows good agreement between the two sets of results. Furthermore, by combining the parabolic rate law of diffusion and the equation for the intergranular oxygen diffusion depth, an explicit expression for the oxygen diffusivity of grain boundaries is derived. It is found that this diffusivity is both a ΔK- and a frequency-dependent parameter.

Environmental interactions in high-temperature fatigue crack growth of Ti-1100

The crack growth behavior of Ti-1100 is investigated for loading frequencies ranging from 30 to 0.0031 Hz at temperature levels extending from 23 °C to 650 °C in both air and vacuum environments. Two types of time-dependent damage mechanisms have been identified: oxidation and creep effects. It is concluded that the effect of oxidation on the crack growth acceleration is rapidly developed and only weakly dependent on total cycle time. Creep effects, on the other hand, are dominant at low frequencies in both air and vacuum and are loading rate dependent. The degree of contribution of each of these two damage modes during the steady state growth region has been phenomenologically determined by examining the frequency dependence on the exponent and coefficient parameters of the Paris-type crack growth equation. It is found that these parameters are largely determined by the extent of the viscoplastic response of the crack tip region below a specific, environment-sensitive transition loading frequency. Furthermore, the physical mechanisms involved in the environment-affected damage are identified with the nature of crack tip plastic work input as a function of loading frequency. The influence of frequency and environment on the anomalous appearance of pronounced stage I/stage II knee regions is also discussed with respect to closure levels and creep transient response.

Frequency effects on fatigue crack growth behavior in a near-α titanium alloy

Abstract The loading frequency effects on elevated temperature fatigue crack growth behavior in a new near-α, β-processed titanium alloy were examined in both air and vacuum environments. The individual influences of environment and creep are identified in terms of both the macroscopic crack growth rates and detailed fractographic observations as a function of the applied ΔK. Results indicate the existence of two regions of transgranular crack growth: microstructurally sensitive and insensitive. The transition between these two regions was found to depend on the testing temperature. Lower frequencies promoted an increase in cleavage fracture while an addition of hold time at maximum load resulted in prior β grain boundary fracture attributed to creep damage. In addition, the transition to intergranular fracture at high ΔK was found to take place at higher frequencies in vacuum, yielding a higher crack growth rate than in air which is indicative of a faster, more widespread viscoplastic flow without the presence of oxidation. Closure measurements indicated a dominant influence of asperity-induced closure in non-oxidizing environments and at low values of applied ΔK.

Effects of aging on the tensile and fatigue behavior of the near-α Ti-1100 at room temperature and 593 °C

Abstract Long term aging of Ti-1100 alloy at its intended service temperature of 593 °C results in the formation of two types of precipitates, Ti 3 Al and (TiZr) 6 Si 3 . The effect of aging times corresponding to the conditions of unaged, peak aged (10 000 min), and overaged (>60 000 min) on tensile behavior is studied at two test temperatures: room temperature and 593 °C. Aging produces an increase in yield strength and a decrease in ductility at both test temperatures. The decrease in ductility is much more pronounced at room temperature than at 593 °C. Aging also suppresses the appearance of serrations associated with dynamic strain aging in the plastic portion of the tensile curve at 593 °C. However, another feature of dynamic strain aging, namely a lack of strain rate effect on yield, is not substantially changed by the aging process. The effect of aging on fatigue crack growth rates (FCGR) at room temperature and 593 °C is also examined. Aging increases FCGR at room temperature but produces a slight decrease in FCGR at 593 °C.

Probabilistic description of fatigue crack growth in polycrystalline solids

Abstract A stochastic model describing the crack evolution and scatter associated with the crack propagation process has been built on the basis of the discontinuous Markovian process. The evolution and scatter are identified in terms of constant probability curves whose equation is derived as In P r (i) = B(e KI 0 − e Ki ) , i ≥ I 0 , where i is the number of cycles, B and K are crack-length-dependent variables, P r (i) is the probabiliity of the crack being at position r along the fracture surface after i cycles elapse and I 0 is the minimum number of cycles required for the crack to advance from one position on the fracture surface to the next. The validity of the model is established by comparing the crack growth curves generated for Al 2024-T3 at a specific loading condition with those experimentally obtained.

Microstructural changes during aging of a near-α titanium alloy

Abstract This paper describes the evolution of precipitation at a selected aging temperature of 593 °C in a new silicon-bearing near-α titanium alloy designated Ti-1100. This particular aging temperature was chosen to simulate the aging process occurring during service in a gas turbine engine. Over-aging results in the formation of silicide precipitates along the α platelet boundaries and the formation of Ti 3 Al distributed homogeneously throughout the matrix. The overall hardness response with aging exhibits two peaks: a minor peak at 800 min and a major peak at 10 000 min. Transmission electron microscopy evidence suggests that the silicide forms prior to the Ti 3 Al and that the minor peak is associated with silicide formation. The major peak is related to the silicide and/or Ti 3 Al. Metallurgical stability is only achieved after 60 000 min aging time. Since precipitation occurs over both short and long time periods (800–60 000 min), aging effects should be considered when characterizing high temperature mechanical behavior in this and similar near-α titanium alloys.