Nasgro Fracture Mechanics And Fatigue ((NEW)) Crack Growth Analysis Software
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A crack in a part will grow under conditions of cyclic applied loading, or under a steady load in a hostile chemical environment. Crack growth due to cyclic loading is called fatigue crack growth and is the focus of this page. Crack growth in a hostile environment is called environmental crack growth and is not discussed here.
The analysis of fatigue crack growth relies on the concepts of fracture mechanics which are discussed on this page. If you are not familiar with fracture mechanics, it is recommended that you read that page before proceeding.
There are typically tails at the upper and lower ends of the growth rate curve. The tail at the lower end for small values of ΔK (region I) approaches a vertical asymptote called the fatigue crack growth threshold, ΔKth. Crack growth does not typically occur for stress intensity ranges below the threshold.
The tail at the upper end of the curve for large values of ΔK (region III) also approaches a vertical asymptote. When the stress intensity ratio R is equal to 0, corresponding to zero-to-tension loading, the vertical asymptote at the upper range of the curve is the critical stress intensity for the material. Recall that for thick sections, this critical stress intensity is the plane-strain fracture toughness. This upper tail in the high ΔK region signifies accelerating crack growth. Cracks in this region grow in a rapid and unstable manner until failure occurs.
In the case that the number of cycles experienced during service is too large as compared to the expected number of cycles to failure, periodic inspections may be required to ensure that cracks do not grow to the point that they become critical. The inspection period should be chosen at some fraction of the expected time to failure. Cracks detected during inspection may be repaired. If repair is impractical, then crack growth analysis should be performed to determine the expected cycles to grow the detected crack to failure. The results of the analysis may indicate that part replacement is necessary.
Some systems may be designed to allow for some crack growth before repair and replacement. In this case, fatigue crack growth analysis is key to safe operation of the system. This approach to allowing and accounting for a safe level of crack growth during the operation of the system is referred to as damage-tolerant design.
Existing studies [4,10,11] revealed that the creep-fatigue crack growth (CFCG) behavior is significantly affected by temperature, applied stress, dwell time, and their conjoined effects. To date, a considerable number of investigations focusing on the mechanisms of crack growth have been carried out, supporting the construction of predicting models. Fatigue damage occurs as the material undergoes cyclic stress, while creep damage occurs when the material is subjected to sustained loading conditions. The total damage of creep-fatigue failure is determined by fatigue, creep, and their interaction. The proportion of each term depends on the environmental and loading condition, contributing to the main challenge of description on creep-fatigue crack growth behavior.
Basically, it is widely accepted that the time-dependent creep damage leads to intergranular crack growth, while the cycle-dependent fatigue damage contributes to transgranular crack growth. However, the truth turns out to be more complicated. Sadananda et al. revealed that the predominant fracture mode of Inconel-718 was intergranular at lower stress intensity levels, while transgranular at higher stress intensity levels (>60 MPa·m0.5) at 540 °C with 0 s and 60 s dwell time [12]. However, they found that transparent failure mode changed from transgranular to intergranular as the stress intensity level increases for Udmet-700 at 800 °C with 60 s dwell time [7]. Moreover, as for an identical DA Inconel-718 material, the fracture mode altered from transgranular to intergranular as temperature decreased from 700 °C to 550 °C when the local stress level exceeds the fracture toughness at the crack tip [8,13]. Therefore, it is of great importance to reveal the inherent mechanism for the alternate fracture mode depending on stress intensity levels at elevated temperatures.
The mechanism of crack growth affected by creep-fatigue interaction has been systematically investigated, where the form of creep damage varies significantly according to the level of stress intensity [5,14]. A general description can be established as (1) lower stress intensity levels: creep damage occurs at grain boundaries, where voids nucleation and growth dominate the crack growth behavior; (2) medium stress intensity levels: creep damage leads to crack blunting, while grain boundary separation motivates the crack propagation; and (3) higher stress intensity levels: creep damage is manifested by the nucleation of growth of voids in crystal, especially around inclusions or secondary phases, while the crack merging accelerates the crack growth rate.
Besides the creep damage mechanism, the crack-tip plastic zone size serves as another important factor that affects the creep-fatigue crack growth. As for a small cyclic plastic zone that is constrained to a limited number of grains, a shear-dominated crack growth occurs along the principal slip direction. When the cyclic plastic zone enlarges to the scale containing several grains, the crack growth is influenced by the double-slip mechanism. When the cyclic plastic zone derived from fatigue damage comes with the creep damage, the creep-fatigue interaction might accelerate or slow the crack growth, which depends on the dislocation slip at elevated temperatures [15,16], as well as the voids in grain boundaries [17] and secondary phases [18,19]. Therefore, the representation of time-dependent creep damage and cycle-dependent fatigue damage, and their interaction, becomes the main task in crack growth rate modeling for high-temperature structures.
The accurate description of crack growth behavior depends on two aspects: the first is the selection of dominant factor in fracture mechanics to correlate the stress-strain field around the crack tip, and the second is the establishment of proper format to relate the crack growth rate to the dominant factor. As for the small-scale yielding condition, the stress intensity factor K is always selected as the dominant factor. However, when the inelastic component of deformation is too large to be ignored, the usage of K is no more sufficient to describe the fracture process, leading to two kinds of approaches to ensure the accuracy of crack growth rate prediction. The first one is to develop a new factor to include the inelastic deformation, i.e., C* for extensive creep conditions [20], and C(t) for transparent creep conditions [21]. To obtain an accurate estimation of C* or C(t), visco-plastic constitutive models were developed to calculate the stress-stain field around the crack tip, as represented by the works of Landes and Begley [22], Goldman and Hutchinson [23]. Afterwards, damage parameters were introduced into the constitutive models to represent a more comprehensive creep state, such as the single damage variable models [24,25,26,27,28,29,30], double damage variable models [31,32], and triple damage variable models [33,34]. Although these C*- or C(t)-based models were quite persuasive due to the explicit physical meaning of creep deformation, it has not been adopted in practical engineering applications because of the limitation of creep constitutive models.
Therefore, aiming at an accurate prediction in crack growth rate of materials at elevated temperatures, scholars have proposed several phenomenological models and different control parameters to elaborate the stress-strain field of crack tip. From a general standpoint, these models can be divided into three categories [35]. The first one was the mononomial model, which merely focused on a single failure mode, such as the fatigue crack growth (FCG). The second one was the binomial model based on linear superposition, which included both the effects from cycle- and creep-dependence. The third one was the trinomial model that added the interaction term to the binomial model, resulting in a more comprehensive and capable predictor for creep-fatigue crack growth. Due to the complex conjoined effects from high temperature, dwell time, and micro-mechanism of fracture, there are no universally accepted rules or analytical models for describing the creep-fatigue crack growth rates at high temperatures.
Experimental results of creep-fatigue crack growth at elevated temperatures. (a) T = 600 °C, R = 0.1; (b) T = 600 °C, R = 0.5; (c) T = 700 °C, R = 0.1; (d) T = 700 °C, R = 0.5.
The most classical fatigue crack growth model is the Paris law [36], which describes the relation between crack growth rate da/dN and the stress intensity factor range ΔK by a simple power law formula. Due to the concise form of equation, it became the most widely used empirical prediction for fatigue crack growth rate in engineering applications. Further development of crack growth models were mostly based on the Paris law.
where fN is the Newman crack closure function, R is the stress ratio, Kth and Kc are the crack growth threshold and fracture toughness respectively, C, n, p, q are the fitting parameters. The function fN can be further represented by [39]
Byrne et al. [43] conducted creep-fatigue crack growth experiments on Waspaloy alloy. By using the Paris law to describe the fatigue crack growth rate, and a creep term consisted of ΔK, R, and th, da/dN was expressed as
By dividing the fatigue crack growth data with the established model for stage II, i.e., the Paris model with parameters in Table 4, the value of function f3 on each data point can be accordingly determined, as illustrated in Figure 5. Through a fitting process, parameter Kc and q can be determined, by which the fitting curves are marked blue. However, the original term in the NASGRO model underestimates the effect of f3 as Kmax approaches Kc. Therefore, a new format of f3 is constructed, as enlightened by the NASGRO model, which can be expressed as 2b1af7f3a8