Threshold ΔKth Research Articles

Investigation of fracture mechanical properties of a brass alloy with microstructural variations

This study investigates the effect of microstructural variations on the mechanical properties of CuZn35Mn2Al1Fe1-C-GS brass alloy. Specimens taken from positions with different cooling rates in a large cast component exhibit coarse-grained (approximately 5mm) and fine-grained (approximately 1mm) microstructures. Fine-grained samples demonstrate at least a 7% increase in Ultimate Tensile Strength (UTS) and up to a 33% higher long crack threshold ΔKth,lc. Hardness measurements are similar between microstructures. The NASGRO model and cyclic R-curve are applied to fit crack propagation data, and fractographic analysis reveals distinct fracture mechanisms. The results indicate that a fine-grained microstructure enhances tensile strength and crack resistance, providing valuable insights for the design and maintenance of heavy machinery components made from cast brass.

On the Link between Plastic Wake Induced Crack Closure and the Fatigue Threshold

This purpose of this paper is to examine the relationship between crack growth equations based on Elber’s original plastic wake induced crack closure concept and the fatigue threshold as defined by the American Society for Testing and Materials (ASTM) fatigue test standard ASTM E647-15el. It is shown that, for a number of conventionally manufactured metals, the function U(R), where R is the ratio of the minimum to maximum applied remote stress, that is used to relate the stress intensity factor ΔK to the effective stress intensity factor ΔKeff is inversely proportional to the fatigue threshold ΔKth(R). This finding also results in a simple closed form equation that relates the crack opening stress intensity factor Ko(R) to ΔK, Kmax, and the fatigue threshold terms ΔKth(R) and ΔKeff,th. It is also shown that plotting da/dN as function of ΔK/ΔKth(R) would appear to have the potential to help to identify the key fracture mechanics parameters that characterise the effect of test temperature on crack growth. As such, for conventionally manufactured metals, plotting da/dN as function of ΔK/ΔKth(R) would appear to be a useful addition to the tools available to assess the fracture mechanics parameters affecting crack growth.

On 50 years of fatigue crack closure dispute

AbstractIn this article, we examine the 50 years of observations and interpretations into the subject of fatigue crack closure in lab air and aqueous solutions: disputes and implications. Over this period, several closure concepts have been invoked to explain why the crack propagation threshold ΔKth should reduce with load ratio R. Among these, three types are the most popular and these are closure induced by crack (i) plasticity (PICC), (ii) oxides (OICC), and (iii) roughness (RICC). Therefore, these three and their role in shielding the fatigue crack tip are critically examined. This analysis finds that the reduction in ΔKth with increasing R‐ratio in lab air and aqueous solutions is weakly linked to decreasing crack closure behind the crack tip but strongly related to the access of the environment to the crack tip region and its influence on fatigue damage at and ahead of the crack tip. Supporting evidence for this interpretation comes from the lack of ΔKth dependence on R in a good vacuum (with partial pressure of 10−5 Pa or less). In chemical environments, our viewpoint is supported by a critical analysis of corrosion processes that found that there is insufficient time for most metallic species to form ions, hydrolyze, and transform into hard phases at the crack tip before closure. Therefore, when closure occurs at the crack tip, most of the oxidized metallic species will exist as aquo‐complexes, gel, or colloids that have insufficient shear strength to wedge crack faces during unloading.

Roughness induced crack Closure: A review of key points

In this article we review and discuss the key points on the roughness induced closure (RICC) that is considered to affect crack tip shielding. While the RICC has been suggested as a mechanical obstruction in the wake of the crack during cyclic unloading for planar slip alloys at the threshold region, the emphasis on the access of the environment to the crack tip for an environmental damage was not considered. The question is how much the role of RICC alone versus the environment that can affect the overall damage needs some discussion. Dislocation-based models have indicated that the crack tip shielding effect from a single asperity is small. In addition, the location of such an asperity (rigid or deformable) behind the crack tip and multiple asperities also affects the shielding. Existing examples of threshold ΔKth data in a good vacuum (less than10-5 Pa) suggest that RICC is not a significant factor to reduce ΔKth with R in planar slip alloys at ambient temperature. The same alloy in moist air/dilute chemical environment do exhibit ΔKth reduction with R. This comparative observation indicates that the factor of environmental access dominates in the crack opening behind the crack tip affecting the near threshold region for fatigue damage. Near threshold region is where the time dependent environmental damage is significant.

Influence of SiC particles orientation on fretting crack extension in an Al-SiC metal matrix composite

The effect of SiC particle orientation regarding the fretting cracking process of an Al-SiC metal matrix composite (MMC) is investigated. Focusing on the crack extension below a sphere-on-flat fretting contact after 106 loading cycles, it is shown that the maximum crack extension is observed when the SiC particles are collinear with the crack path (i.e. perpendicular to the fretting tensile stress). The minimum extension is by contrast observed when the SiC particles are perpendicular to this latter. The crack extension seems favoured when the crack path follows the interface between the SiC particle and the Al matrix but slows down when the particles are perpendicular to the crack path. The crack must then fracture the reinforcing particle. These various experiments are simulated using a 3D finite element modelling (FEM) including the presence of a 3D crack shape. Considering that the crack arrest condition is reached (i.e. plain fretting cracks do not extend anymore after 106 loading cycles), the crack arrest thresholds ΔKth from short to long crack regimes as a function of the SiC particles orientation are extracted from a reverse analysis of the experiments.

Fatigue crack propagation behavior of multiphase microstructure in a quenched and partitioned medium‐carbon bainitic steel

AbstractA medium‐carbon steel was treated by the bainitic isothermal transformation plus quenching and partitioning (B‐QP) process to obtain bainite/martensite/retained austenite multiphase microstructure, and its fatigue crack propagation (FCP) behavior was evaluated in contrast with BAT (bainite austempering) sample with fully bainite microstructure. Results show that B‐QP sample exhibits a lower FCP rate and higher fatigue threshold ΔKth (12.6 MPa·m1/2). Moreover, the FCP path of B‐QP sample displays a strongly tortuosity and more crack branching due to more filmy retained austenite (7.2%) and higher percentage of high angle misoriented boundaries (68%). The larger crack tortuosity and the secondary cracks as result of crack branching are primarily responsible for the lower FCP rate of B‐QP sample. In addition, the FCP rate curve of B‐QP sample shows a pronounced small plateauing at the near‐threshold zone, which can be ascribed to the mechanical twinning that occurred in the filmy retained austenite.

Determining of the Fatigue Crack Growth Rate of HSLA Steel at Room Temperature

Welded joint is a critical region of a welded structure and fracture mechanics analysis is inevitable in the structural integrity assessment of all welded structures. This paper shows the determining of parameters of the fatigue crack for constituents of welded joints produced of high strength low alloyed steel. The applied methodology refers to the Paris relation where the link was established between the variable load quantity or the corresponding stress intensity factor range and crack growth per cycle. Results have shown that the position of the notch and crack initiation affect the values of the stress intensity range of fatigue threshold ΔKth and parameters in the Paris’ equation. This is mostly expressed when determining growth parameters of the fatigue crack in heat affected zone of HSLA steel, where different changes of growth speed of the fatigue crack clearly express differences in structure of the crack pass.

Implications of ΔK‐Rratio in vacuum

AbstractIn this article we discuss the high vacuum implications on the role of positive load ratios (R = Pmin/Pmax) on the threshold ΔKthand fatigue crack growth (FCG) behavior in commercial alloys. It is experimentally observed that the ΔKthis independent ofRin vacuum. Also, for a given applied ΔK, FCG rate is weakly dependent ofRover the entire range of crack growth rates for several alloys. In addition, limited data on both short and long crack FCG in vacuum results fall within the same experimental scatter suggesting that a typical small crack FCG effect observed in lab air was insignificant or diminished in vacuum. A marginalR‐ratio effects on ΔKthin vacuum are seen for materials with different microstructures, yield strengths, elastic modulus, work hardening properties, and slip modes. The provided analysis and examples seem to imply that FCG in vacuum be primarily dependent on applied ΔK that comes from mechanical driving force. Possible mechanistic explanations are given.

Machine learning predicts fretting and fatigue key mechanical properties

The present work uses machine learning to predict fretting crack lengths and corresponding stress intensity factors (SIF) under partial slip conditions resulting in crack arrest. Plain fretting tests were first performed on cylinder/flat configurations in partial slip, in which the test sample was flat. Adjusting contact pressure and cylinder radius, both short and long crack arrest responses were achieved for the studied C-Mn steel. Finite element (FE) analysis was then used to compute the fretting SIF threshold ΔKth for each arrested cylinder/plane fretting crack condition. Under elastic fretting conditions, a coupled approach combining complete FE simulations modeling the crack and Rice's fracture integrals was used. When plasticity needed to be considered, an indirect method was applied, using FE simulations without the crack and classical weight functions once elastic shakedown was reached (decoupled approach). The fretting SIF threshold ΔKth could then be extrapolated to estimate the fatigue long crack SIF threshold ΔK0 when the fretting crack was long enough. The novelty of this research work resides in the use of Machine Learning to predict the key mechanical parameters introduced above. A backpropagation algorithm with Bayesian regularization was used to identify a shallow neural network model based on just fourteen experiments. A neural network-based model was then employed to describe fretting crack lengths and corresponding SIF of the studied alloy as a function of the fretting contact radius, the maximum surface pressure, and shear traction. Perfect correlations were obtained to predict both crack depth and associated SIF threshold. An investigation was performed to determine the reliability with which samples sizes matching the count of the available experimental points can be used to predict fretting crack lengths and corresponding SIF. A Monte-Carlo bootstrapping method was used to estimate the output confidence interval corresponding to specific target inputs. This analysis provided optimistic results as relatively small datasets may be sufficient for accurate predictions. The neural network described short to long crack behaviors under elastic or elastoplastic conditions, making it a valuable tool for predicting fatigue long crack ΔK0 based on fretting experiments.

A Review of Fatigue Crack Growth Thresholds for Metals in Fitness-for-Service Codes: On the Uncertainty of Using the Thresholds at Negative Stress Ratios

Abstract Fatigue crack growth thresholds ΔKth for metals are provided in many fitness-for-service codes. However, fatigue crack growth thresholds at negative stress ratios are not consistently defined. There are two forms of thresholds at negative stress ratios: constant thresholds irrespective of stress ratios, or increasing thresholds with decreasing stress ratios. The definitions of the thresholds at negative stress ratios also take two forms: either ΔKth = Kmax−Kmin, or ΔKth = Kmax. ASME Section VIII, Section XI (ferritic steel) and International Institute of Welding (IIW) give constant thresholds expressed by ΔKth = Kmax. American Petroleum Institute (API) 579 and ASME Section XI (stainless steel) give increases in thresholds with decreasing stress ratios and the thresholds are expressed by ΔKth = Kmax−Kmin. British Standard (BS) 7910 gives constant thresholds expressed by ΔKth = Kmax−Kmin. The fatigue crack growth thresholds differ significantly among different fitness-for-service (FFS) codes. Appropriate thresholds for ferritic steels, stainless steels, and aluminum alloys are demonstrated in the literature survey.

Artificial aging time influencing the crack propagation behavior of the aluminum alloy 6060 processed by equal channel angular pressing

The combination of a severe plastic deformation (SPD) by equal-channel angular pressing (ECAP) with a subsequent heat treatment significantly influences the precipitation characteristics of age-hardenable aluminum alloys. The aging kinetics is accelerated and the morphology of the precipitates is affected by the induced strain. In the present study, the influence of the artificial aging time and the resulting precipitation morphology on the fatigue threshold was investigated for the aluminum alloy 6060 with conventional grain size (CG) and after ECAP processing. Four artificial aging conditions are compared for the as-extruded and ECAP processed material, respectively. The resulting microstructure is examined by transmission (TEM) and scanning transmission electron microscopy (STEM) and related to the processing condition and the aging time. The mechanical properties are characterized by tensile and hardness testing and crack propagation tests are conducted in order to determine the threshold ΔKth. The ECAP processed conditions exhibit a lower resistance against crack propagation regardless of the aging time, when compared to the as-extruded conditions. Therefore, the grain size is determined as the major influencing factor on the fatigue threshold. In contrast, the effect of the aging time and the precipitation morphology is only minor. When compared to incoherent precipitates, coherent ones promote planar slip resulting in an increased threshold against crack propagation for both CG and finer grained, bimodal microstructures. However, the size of the coherent precipitates and the resulting lattice distortion is decisive to achieve higher fatigue thresholds.

A modification to the two driving forces model for fatigue threshold prediction

The two driving forces (TDF) model was modified based on the dislocation dipoles mechanism of fatigue crack growth (FCG) and corrected by Kmax effect for a better prediction of the R dependent FCG thresholds ΔKth and Kmax,th. This model can well describe transformation of the crack growth mechanism from fatigue fracture to quasi-static fracture when R tends to 1, and agrees well with experimental data for a broad round of alloy systems. An empirical relationship between the fatigue threshold and the fracture toughness was proposed, and then an approximately material-independent fatigue threshold prediction model was established by normalization based on this relationship.

Influence of Cu precipitates and C content on the defect tolerance of steels

Understanding the effects of microstructural defects, which can have a high impact on service life, is of great importance in the design of cyclically loaded components. For this, the size of the defect as well as the material’s ability to counteract microstructural defects have to be considered. In this study, the defect tolerance of differently heat-treated Cu alloyed steels with two different C contents (0.005 and 0.21 wt% C) has been investigated by testing specimens with artificial defects. From the results of fatigue experiments, defect tolerance is assessed based on different approaches: (i) a comparison of stress intensities, derived from Murakami’s √area approach, (ii) comparing fatigue lifetime for a given defect size and stress amplitude, (iii) the reduction of fatigue strength by a defect for a given defect size, and (iv) using the Kitagawa-Takahashi diagram, enabling the calculation of the critical defect size √area0 as well as fatigue crack propagation threshold ΔKth,calc. The results show that for the 0.005 wt% C steel an increase in aging time is accompanied by an increase in defect tolerance, which correlates with a higher cyclic hardening potential induced by the formation of Cu precipitates. However, the results show that strength and ductility also influence defect tolerance. By using the short-time procedure PhyBaLCHT, which is based on cyclic indentation tests, all these factors influencing defect tolerance can be determined efficiently. The 0.21 wt% C steel does not reveal an improved defect tolerance which is presumably caused by the dominating pearlite phase.

Failure analysis on pre-corroded specimens of Inconel alloy 718, under ultrasonic fatigue tests at room temperature

This work deals with the pre-corrosion effects on the ultrasonic fatigue endurance failure of Inconel alloy 718 (I-718), and on crack initiation and propagation at room temperature. Pre-corrosion was induced using the international standard ESA ECSS-Q-ST-70-37C of the European Space Agency. The base and pre-corroded specimens were tested under the ultrasonic fatigue technique at frequency of 20 kHz, room temperature, without control of environmental humidity and with the load ratio R = -1. The results of ultrasonic fatigue endurance show that at higher levels of stresses, up to 746 MPa, the pre-corroded specimens show a lower fatigue endurance with a factor of 10 approximately, compared with the base material. In addition, the principal trends of pitting at the specimen neck section were reproduced by numerical models in order to investigate the stress concentration factors and its impact in fatigue endurance. Finally, the stress intensity factor in mode I was evaluated numerically at the specimen neck section from crack initiation to fracture and the stress intensity factor range threshold ΔKTH was obtained for the two type of tested specimens, together with the number of cycles in the “Stable Zone of Crack Growth”, for both types of specimens.

Ultrasonic and Conventional Fatigue Endurance of Aeronautical Aluminum Alloy 7075-T6, with Artificial and Induced Pre-Corrosion

Ultrasonic and conventional fatigue tests were carried out on the AISI-SAE AA7075-T6 aluminum alloy, in order to evaluate the effect of artificial and induced pre-corrosion. Artificial pre-corrosion was obtained by two hemispherical pitting holes of 500-μm diameter at the specimen neck section, machined following the longitudinal or transverse direction of the testing specimen. Induced pre-corrosion was achieved using the international standard ESA ECSS-Q-ST-70-37C of the European Space Agency. Specimens were tested under ultrasonic fatigue technique at frequency of 20 kHz and under conventional fatigue at frequency of 20 Hz. The two applied load ratios were: R = −1 in ultrasonic fatigue tests and R = 0.1 in conventional fatigue tests. The main results were the effects of artificial and induced pre-corrosion on the fatigue endurance, together with the surface roughness modification after the conventional fatigue tests. Crack initiation and propagation were analyzed and numeric models were constructed to investigate the stress concentration associated with pre-corrosion pits, together with the evaluation of the stress intensity factor in mode I from crack initiation to fracture. Finally, the stress intensity factor range threshold ΔKTH was obtained for the base material and specimens with two hemispherical pits in transverse direction.

Fracture mechanics behavior of TiNbSn alloys as a function of alloy content, cold working and aging

Mechanical properties such as tensile strength, ductility and elastic modulus, which are directly related to fracture mechanics characteristics, can be controlled during termo-mechanical manufacture of TiNbSn alloys. Cold working the alloys reduces its ductility and elastic modulus. Aging reduces their ductility further, but increases their elastic modulus. The present study aims to evaluate the effect of Nb (35% and 42% wt.) and Sn (0% and 2.5% wt.) contents on fracture toughness and fatigue crack growth of TiNbSn alloys of both cold worked and aged at 400 °C. The fracture toughness KIC was performed, and fracture analysis allowed to evaluate micromechanics changes. Crack growth rate(da/dN–ΔK) tests were also performed. Aging was beneficial to fracture threshold ΔKth and crack growth rate of the alloys. However, aging did not interfere with fracture toughness KIC. The increase in Nb content is beneficial to both fracture toughness and crack growth rate of the aged alloys. The addition of Sn in the aged 42% Nb alloy decreases the crack growth rate at higher ΔK. For alloys of similar elastic modulus, the size of dimples is proportional to fracture toughness.

Evaluation of fatigue crack propagation in steel ESET specimens subjected to variable load spectra

This paper reports on an experimental study of fatigue crack growth in steel specimens. First, block loading tests (sequences of low and high stress intensity factor ranges ΔK) are discussed. Limited crack growth retardation occurs at transitions from low to high load ranges; significant retardation or crack arrest are observed in high-low transitions. Next, semi-random load spectra are created, processed using a peak-and-valley analysis and further reduced by removing the load ranges below the stress intensity factor threshold ΔKth. Rainflow counting is performed to obtain load profiles consisting of a sequence of blocks with constant ΔK. For the semi-random and the (reduced) peak-and-valley spectra no significant load interaction is observed. Pronounced crack growth retardation is observed in an ordered spectrum obtained by rainflow counting. The strong reduction in number of cycles of the (reduced) peak-and-valley spectra allows for exploration of accelerated fatigue testing. Experimental results of fatigue crack propagation are compared to results of calculations using a Python based numerical framework.

A probabilistic framework to define the design stress and acceptable defects under combined-cycle fatigue conditions

Probabilistic routines are necessary to determine the permissible design stress when the operational conditions of traditional gas turbines are further challenged to reach higher performances in terms of flexibility. This paper focuses on the definition of a probabilistic tool aimed to simulate the damage development under combined high and low cycle fatigue conditions considering the stochastic nature of some of the variables introduced in the model. The variables considered in the present study are the long crack threshold ΔKth,LC and the slope of the crack growth law C in the so-called Paris region, the endurance limit Δσw0 and the variability of the applied stress as it cannot be considered a fixed variable in the complex loading scenario of gas turbines. A broad experimental campaign was performed to characterize the material properties in terms of short and long crack resistance under constant and combined cyclic conditions. The data were used to define the average and variance of the materials parameters to feed Montecarlo simulations and, at a target probability of failure, establish the design stress. This work points to determine safety margins which strictly depend on the natural variability of the variables that govern the damage accumulation in the mechanical component.

A unified mean stress correction model for fatigue thresholds prediction of metals

Two fatigue characteristic thresholds, i.e. fatigue limit Δσe and fatigue crack propagation threshold ΔKth, have significant mean stress sensitivity. In the work, a new mean stress correction model for the two fatigue thresholds is proposed based on the cyclic strain energy density concept. Extensive experimental data in the literature is unified evenly by the proposed normalized fatigue threshold-R curves. Besides, a comparison of the proposed model with the existing models is carried out, which demonstrates that the present work can achieve more accurate predictions with the advantage of being of easy use and of being independent on any material constant.

Crack growth based life prediction approach under LCF-HCF interaction

Prediction of cyclic life under low cycle fatigue - high cycle fatigue (LCF-HCF) interaction is of paramount importance in the context of structural integrity of components in the primary side of fast reactors where such damage under LCF-HCF interaction occurs. The present investigation deals with the crack growth behavior of a type 316LN austenitic stainless steel subjected to simultaneous application of LCF and HCF cycles (block-loading). Tests were performed over a wide range of temperatures from ambient to 923 K. Experimental results indicate that a critical crack-length (acr) exists, beyond which the LCF-HCF interaction becomes significant. An attempt was made to predict life under block cycling by estimating the acr using fatigue crack threshold (ΔKth) since the latter is known to be affected significantly by the loading history. A universal equation, based on the concept of an equivalent critical crack length (acr.,eq) which incorporates the damage contribution from DSA and ratcheting under combined LCF-HCF loading, was proposed for life estimation.