Growth Rate Behavior Research Articles

Fatigue crack growth rate behaviour of aluminium matrix composites reinforced with hollow glass microsphere

This study investigates nanoindentation and fatigue crack growth rates of pure aluminium and aluminium hollow glass microsphere metal matrix composite (Al + HGM MMCs) cast plates. Using the stir casting method, pure aluminium, and Al + HGM MMCs were fabricated with hollow glass microsphere (HGM) additions ranging from 5 % to 30 % by weight. Nanoindentation techniques were utilized to assess fundamental mechanical properties such as hardness and elastic modulus. This study primarily focuses on analyzing fatigue crack growth behaviour within the linear region of da/dN vs. ΔK graphs for these stir-cast plates. Chevron-notch CT specimens were prepared following ASTM E-647 standards, and the constant amplitude increasing ΔK method was employed to generate Paris curves. Furthermore, the research investigated the influence of stress ratios (R=0.1, 0.2, and 0.3) on the fatigue crack growth rate in both Pure Al and Al + HGM MMCs. The study also determined the threshold and critical stress intensity factor ranges (ΔKth and ΔKc) for these plates. Additionally, Paris constants (C, m) were calculated to characterize the fatigue behaviour of the cast plates. X-ray diffraction analysis was conducted to reveal dislocation densities, crystalline sizes, and micro-strain responses of the fatigue-fractured specimens. Moreover, SEM fractography analysis provided insights into the fracture behaviour and crack branching observed in both pure aluminium and Al + HGM MMCs plates.

A Model to Account for the Effects of Load Ratio and Hydrogen Pressure on the Fatigue Crack Growth Behavior of Pressure Vessel Steels.

A phenomenological model for estimating the effects of load ratio R and hydrogen pressure PH2 on the hydrogen-assisted fatigue crack growth rate (HA-FCGR) behavior in the transient and steady-state regimes of pressure vessel steels is described. The "transient regime" is identified with crack growth within a severely embrittled zone of intense plasticity at the crack tip. The "steady-state" behavior is associated with the crack growing into a region of comparatively lower hydrogen concentration located further away from the crack tip. The model treats the effects of R and PH2 as being functionally separable. In the transient regime, the effects of the hydrogen pressure on the HA-FCGR behavior were negligible but were significant in the steady-state regime. The hydrogen concentration in the steady-state region is modeled as being dependent on the kinetics of lattice diffusion, which is sensitive to pressure. Experimental HA-FCGR data from the literature were used to validate the model. The new model was shown to be valid over a wide range of conditions that ranged between -1≤R≤0.8 and 0.02≤PH2≤103 MPa for pressure vessel steels.

Investigating the effect of stress ratio on fatigue crack growth rate behaviour in friction stir welded AA7075-T651 aluminium alloy plates

This study examines the characteristics of Fatigue Crack Growth Rate (FCGR) in AA 7075-T651 Friction Stir Welded (FSW) joints with a thickness of 16 mm. Compact tension (CT) specimens from both the base and the FSW joints were utilized to assess FCGR under various stress ratios (0.2 to 0.5). Additionally, the study involved analyzing the transverse tensile characteristics of both the based and the welded joints. The microstructures of the welds were inspected using optical and transmission electron microscopes. Findings indicate that the FSWjoint critical stress intensity factor range (ΔKcr)is lower than the unwelded base, that can be related to precipitates dissolving in the weld zone when the friction stir welding process. Consequently, in contrast to the unwelded base, the fatigue life of AA 7075-T651 aluminium alloy FSW joints is significantly reduced. A scanning electron microscope carried out microstructural analyses of the fracture surfaces of the FSW and base under various stress ratioconditions. The results showed that, in contrast to the parent material, the FSW joint has ultra-fine grains resulting in intergranular cracks in the propagation zone.

Viability of WAAM for fabrication/repair of SS316: Fatigue crack growth behavior for varied notch locations in the vicinity of WAAM-substrate interface

The tensile and fatigue crack growth rate (FCGR) behavior of SS316L wire deposited on SS316 substrate using wire arc additive manufacturing (WAAM) was studied to assess its potential for fabrication and repair applications. Five initial notch locations near the WAAM-substrate interface were considered for FCGR. Cracks in the deposition direction propagated towards the WAAM region. FCGR of cracks in the build direction accelerated in the WAAM region due to its favorable columnar grain orientation. Overall, FCGR behavior near the WAAM-substrate interface is comparable with wrought alloy, suggesting WAAM’s viability for SS316 fabrication and repair, with satisfactory structural integrity observed in tensile and FCGR behavior.

Investigations of fatigue crack growth rate behaviour and life prediction of Si3N4/TiB2 reinforced hybrid metal matrix composites

Many engineering structures and components experience complex fatigue loading throughout their operational lifespan. Economically, it is crucial to forecast the remaining lifespan to prevent catastrophic failure by implementing appropriate inspection schedules. The aim of present work is to investigate the fatigue, and fracture performances of AA7075 alloy-based hybrid MMCs containing Si3N4/TiB2 reinforcement. The composite samples are made by a liquid-state stir-casting process. The study examines the fatigue characteristics of manufactured Hybrid Metal Matrix Composites (HMMCs) by analyzing fatigue crack propagation and fracture toughness under constant amplitude loading with a uniform load ratio of 0.1. The potential influence of reinforcement particles on the fatigue durability of HMMCs was predicted through the application of an 'Exponential Model'. A comparison between the model's performance and experimental findings is carried out. The study suggests that the exponential model accurately predicts fatigue life, showing a maximum percentage deviation of −4.96 %, in close agreement with experimental findings. The fatigue crack growth rate (da/dN) and crack opening displacement (COD) of HMMC indicate that the fatigue life and fracture toughness improve with increase in TiB2 content, up to 6 wt.%. The fabricated HMMC with 4 wt.% Si3N4 and 6 wt.% TiB2 particulates demonstrated the highest resistance to fracture and longest fatigue life among others HMMCs and base alloy.

Application of Machine Learning (ML)-based multi-classifications to identify corrosion fatigue cracking phenomena in Naval steel weldments

Corrosion fatigue (CF) crack detection in welded ship hull structures is quite crucial as well as challenging for ensuring their structural integrity. This is conventionally done by offline ship hull survey and inspection methods, which have large time and cost implications. Data-driven approaches of ship hull crack detection are promising in this regard. Corrosion fatigue crack growth rate (CFCGR) behaviour of shipbuilding steel was studied for its base metal (BM), fatigue-prone heat affected zones (HAZs) of Submerged Arc Welding (SAW), and shielded metal arc welding (SMAW) joints of Naval-grade steel. The results indicated the highest CFCGR for BM, intermediate for SAW, and smallest for SMAW welds. This was attributed to 44% lath martensite observed in the SMAW HAZ microstructure as compared to 33% in SAW HAZ. A novel ML-based method has been proposed for CF crack location identification by a multi-classification approach using CFCGR data for structural health monitoring (SHM) applications. Prediction of crack location (either BM, SMAW HAZ, or SAW HAZ) was investigated using K-nearest neighbour (KNN), linear support vector machine classifier (LSVC), Naïve Bayes (NB), decision tree (DT), random forest (RF), and artificial neural network (ANN) models. DT and RF models were found to perform very well even without scaling and hyper-parameter tuning operations and exhibited 98–99% classification accuracy. Scaling and tuning operations resulted in significant improvements in accuracy of KNN models from 43% to 84% (minmax scaling) and 98% (standard scaling). Significant improvement in the accuracy from 37% to 98% ANN model was achieved by standard scaling. The proposed method shall be useful in data-driven real-time crack location identification in ship hull structures.

Assessing fatigue crack growth thresholds for a Ti-6Al-4V (STOA) alloy using two experimental methods

Fatigue crack growth rate behavior in the threshold and near-threshold regimes for a Ti-6Al-4V solution-treated and over-aged (STOA) alloy was investigated using two test procedures: i) accelerated load reduction (ALR) utilizing faster load-shed rates than recommended in the ASTM standard E647 load-reduction (LR) test procedure, and ii) compression pre-cracking constant-amplitude (CPCA) or load-increasing (CPLI) and load-reduction (CPLR). Fatigue crack growth tests were conducted on compact, C(T), specimens (B = 6.35 mm) with two different widths (W = 51 and 76 mm) at two stress ratios (R = 0.1 and 0.7). The crack-growth-rate test data were compared to previous test data produced from the same batch of material using the ASTM LR and CPCA test procedures that were tested on C(T) specimens (W = 25, 51 and 76 mm) over a wide range in stress ratios (R = 0.1, 0.4, and 0.7).Although none of the load-reduction test procedures provided a good representation of the threshold value (ΔKth) at low R, the CPCA test procedure was the most promising. The LR, ALR, and CPLR test procedures were influenced by prior loading history, leading to higher ΔKth values and slower crack growth rates in the threshold regime due to a rise in the crack-opening loads. The LR and ALR tests at R = 0.1 and shed rates of −0.08, −0.32, and −0.95 mm−1 yielded ΔKth values that were 15 to 38 % higher than the estimated threshold stress-intensity factor range (ΔK*th)R=0.1 based on the crack-closure model (FASTRAN). The compression pre–cracking test procedures are more accurate alternatives for developing threshold and near-threshold fatigue crack growth rates. Specifically, the CPLR test procedure produced a ΔKth value that was 8–18 % higher than (ΔK*th)R=0.1. Additionally, LR and ALR tests produced different ΔKth values as a function of the specimen width for a given load ratio, which violates classical fracture mechanics principles. In addition, the spread in the ΔK-rate data in the low-rate regime was larger than the spread in the mid-rate regime as a function of R, a term referred to as “fanning”. In contrast, the CPCA test procedure produced consistent crack growth rates over the same range of ΔK values examined, independent of the specimen width and these data did not exhibit “fanning” with R. Further research is necessary to develop standard test procedures capable of providing a more definitive representation of the ΔKth value in the threshold regime. However, FASTRAN can serve as a crucial tool in aligning the actual ΔKth values with those obtained through CP testing, thereby bridging the gap and enhancing the reliability of the results.

Temperature-induced disruptive growth rate behavior due to streaming instability in semiconductor quantum plasma with nanoparticles

The nature of the growth rate due to streaming instability in a semiconductor quantum plasma implanted with nanoparticles has been analyzed using the quantum hydrodynamic model. In this study, the intriguing effect of temperature, beam electron speed, and electron-hole density on growth rate and frequency is investigated. The results show that the growth rate demonstrates a nonlinear behavior, strongly linked to the boron implantation, beam electron streaming speed and quantum correction factor. A noteworthy finding in this work is the discontinuous nature of the growth rate of streaming instability in boron implanted semiconducting plasma system. The implantation leads to a gap in the growth rate which further gets enhanced upon increase in concentration of implantation. This behavior is apparent only for a specific range of the ratio of thermal speed of the electrons to that of the holes.

Microstructure, fatigue crack growth rate and low-cycle fatigue behavior of an Al[sbnd]Li alloy sheet with different aging

The microstructures, fatigue crack growth (FCG) rates and low-cycle fatigue (LCF) behaviors of 1445 Al-Li alloy sheet with T6 aging at 170 °C, single-step T8 (S-T8) aging at 150 °C and double-step T8 (D-T8) aging at 170 °C following aging at 150 °C for 4 h were investigated. The main precipitates in T6 and S-T8 samples are δ′ phases, but strain strengthening causes 40 MPa enhancement in the S-T8 sample yield strength (YS). Due to coherent shearable δ′ precipitates, the FCG rate curves of S-T8 samples are highly coincident. With the 2nd-step aging time extension, δ′ precipitates in D-T8 sample gradually coarsen, semi-coherent S′ phases form and their amount increases. The interaction between δ′ precipitates with dislocations transites from shearing to by-passing, leading to the YS enhancement and the FCG resistance decrease. Meanwhile, cyclic-hardening decreases and transfers to cyclic-softening during LCF at starin amplitude of 0.6% ∼ 0.9%. At 0.9% strain amplitude, due to greater cyclic-softening and cleavage fracture of S′ precipitates, the D-T8 sample with 2nd-step aging time of 120 h has a shorter LCF life. The D-T8 sample with 2nd-step aging time of 24 h possesses a comprehensive property of higher strength, lower FCG rate and better LCF life.

Effect of cathodic protection on the corrosion fatigue crack growth behavior and fatigue life of XS-grade shipbuilding steel

Shipbuilding steels are subjected to corrosion fatigue damage phenomena due to conjoint effects of cyclic loading by sea waves and corrosive seawater environment, which often leads to premature failure of ship hull structures. In practice, the impressed current cathodic protection (ICCP) technique is applied to mitigate ship hull corrosion by electrochemically making it cathodic. It is implemented by impressing a direct current to minimize the electrode potential to a predefined protection potential. It is significant to study the effect of ICCP on the corrosion fatigue crack growth rate (CFCGR) behavior and fatigue life assessment of ship hull structures. In this study, CFCGR behavior of high-strength XS-grade shipbuilding steel was investigated in unprotected freely corroding (FC) and protected ICCP (at – 800 mV) conditions using compact-tension specimens at 0.1 Hz frequency in artificial seawater (3.5 wt.% NaCl solution). After crack-closure corrections, it was found that the ICCP-protected specimen (∆KTH = 18 MPa √m) exhibited higher sub-critical or threshold corrosion fatigue crack propagation resistance as compared to the FC specimen (∆KTH = 14 MPa √m). Fractography of the FC specimen revealed the debonding of non-metallic inclusions and formation of micro-pits/secondary cracks as dominant damage mechanisms. ICCP-protected specimen exhibited a signature pattern of parallel secondary cracks and a proportional increase in their density with increasing stress intensity levels during primary crack growth. This fracture morphology indicated the primary-crack branching and further arrest, leading to retarded crack growth rates under ICCP-protection. Fatigue life analysis also confirmed this finding, where the beneficial ICCP-protection effect resulted in at least two times enhancement in fatigue lives from the unprotected FC condition.

Growth kinetics of Lactococcus lactis and Lactobacillus casei in liquid culture medium containing as prebiotics inulin or fructose.

Predictive microbiology is a tool that allows us to evaluate the behavior of the concentration of biomass and estimated cells under extrinsic conditions, providing scientific and industrial benefits. In the present study, the growth of L. lactis and L. casei combined with inulin and fructose was modeled using the Gompertz sigmoidal growth functions and plotted using data obtained from batch culture in relation to biomass and cell concentration expressed as estimates in ln N (OD600nm and cells mL-1 ) as a function of time. The results of the kinetic modeling indicated that (T1) A1B1 = L. lactis + fructose and (T4) A2B2 = L. casei + inulin presented the best function coefficients and best fits in most cases compared to the rest. The specific growth rate of the maximum acceleration was from 0.364 to 0.473 h-1 and 0.100 to 0.129 h-1 , the concentration of bacterial cells (A) was from 0.556 to 0.713 and 0.425 to 0.548 respectively and the time where (μ) occurred with a greater magnitude (L) fluctuated between 0.854 and 0.802 and when this time in (L) is very fast, it presents values of ≤0.072 to ≤0.092. Its coefficient of determination and/or multiple regression (R2 ) obtained in the two adjustments was 0.97. It was possible to predict the influence of the carbon source on the behavior of maximum growth rates, higher consumption due to nutrient affinity and shorter growth time. © 2023 Society of Chemical Industry.

Correlating stress ratio effects on the fatigue crack growth rate behavior of a nickel-based superalloy GTM718

Damage tolerance evaluation under service loads requires a unified constant amplitude fatigue crack growth law for the material which takes care of stress ratio effects. Several types of crack driving force parameters have been proposed in the past to correlate stress ratio effects on fatigue crack growth rates. In the present investigation, a unified crack growth law is derived for a nickel-based superalloy by considering various crack driving force parameters to eliminate stress ratio effects. Initially, the constant amplitude fatigue crack growth rate (FCGR) behavior of GTM718 alloy was experimentally determined at various stress ratios, R ranging from R = 0.1 to 0.7. As expected, increasing the stress ratio, increased crack growth rates, and decreased threshold stress intensity factor range, ΔKth. The conventional crack growth rate, da/dN vs stress intensity factor range, ΔK data was then modified and re-plotted as a function of different crack driving force parameters viz., (a) Elber’s parameter, ΔKeff, (b) Walkers’ parameter, Kw (c) Kujawski’s parameter, K*, (d) Forman’s parameter, Kf, and (e) Two-parameter crack driving force, ΔK*. It was observed that Kf and ΔK* crack driving force parameters were correlating stress ratio effects better than other models in all three regimes of crack growth rates. Further, a unified crack growth law was derived based on the Kf and ΔK* crack driving force parameters which is useful in predicting FCG behavior under service loads.

Evaluation of the growth of maize in monoculture and when associated with peanuts and cassava in the Colombian Amazon

Crop associations are widely recognized as a highly beneficial strategy for agriculture. By combining different crops, optimal production is achieved while minimizing the spread of pests and diseases. This practice offers numerous benefits by allowing maximum utilization of space and mutual adaptation of associated species. It is important to emphasize that crop association is oriented towards the mutual advantage of the species involved, thus guaranteeing favorable results for each of them. In this sense, the behavior of maize growth rates was evaluated in a completely randomized block design with four treatments: maize monoculture; maize and peanut association; maize and cassava association; and maize, peanut, and cassava association. The following variables were evaluated: net assimilation rate (NAR), leaf area index (LAI), relative growth rate (RGR), leaf area ratio (LAR), absolute growth rate (AGR), and leaf area duration (LAD). The association of maize and cassava obtained the highest values NAR (0.002 g cm-2 d-1) and RGR (0.15 g g-1 d-1) compared to the monoculture (0.001 g cm-2 d-1 and 0.08 g g-1 d-1). This happened because maize presented higher leaf production during the vegetative growth stage indicating the physiological efficiency of maize when associated with cassava.

Wind-generated waves on a water layer of finite depth

In this paper, we study the linear stability of a two-dimensional shear flow of an air layer overriding a water layer of finite depth. The air layer is considered to be of an infinite extent with an exponential velocity profile. Three different background conditions are considered in the finite-depth water layer: a quiescent background, a linear velocity profile and a quadratic velocity profile. It is known that the cases of the quiescent water layer and the linear velocity profile allow for analytical treatment. We further provide an analytical solution for the case of the quadratic velocity field: we specifically consider a flow-reversal profile, although the result could be generalized to other quadratic profiles as well. The role of water layer depth on the growth rate of the Miles and rippling instabilities is studied in each of the three cases. Using asymptotic analysis, with the air–water density ratio being a small parameter, we obtain an analytical expression for the growth rate of the Miles mode and discuss the condition for the existence of a long-wave cutoff for these profiles. We provide analytical expressions for the stability boundary in the parameter space of inverse squared Froude number and wavenumber. In scenarios where a long-wave cutoff does not exist, we have carried out a long-wave asymptotic study to obtain the growth rate behaviour in that regime.

Experimental study on the fatigue crack growth rates of welded ultra-high strength steel plates

The assessment of the fatigue crack growth rate behavior of welded structural components made of ultra-high strength steels (UHHS) is very important to gain a comprehensive understanding of these materials under high-cycle fatigue loadings and to enhance their applications in the construction industry. The literature on the fatigue crack growth rates of welded ultra-high strength steel plates with nominal yield strengths higher than 690 MPa is very scarce and only very limited research has been done thus far to provide the Paris’ Law fatigue material constants for welded UHSS components in terms of the base metal (BM), the weld metal (WM), and the heat-affected zone (HAZ) regions, which are essential for fatigue life prediction. Hence, the fatigue crack growth rates of butt-welded UHSS plates with three grades (S700, S960, and S1100) are experimentally investigated in this study using Paris’ Law for these three different regions of the welded components. Gas metal arc welding (GMAW) and laser welding (LW) methods are adopted to analyze the influence of welding methods on each steel grade with respect to their static and fatigue strength, microstructural changes, and hardness. In the fatigue crack growth rate test, it was observed that the S700 base material shows the lowest fatigue crack propagation resistance amongst these three grades. In welded components, laser welding outperforms gas welding in terms of the fatigue crack growth resistance. Comparisons of fatigue crack growth behaviors are made among all three tested UHSSs as well as with those from the literature.

Short-term exposure to near-future CO2has limited influence on the energetics and behaviour of young-of-year salmonids

In many freshwater ecosystems, carbon dioxide (CO2) is increasing. Unknown are the risks that high CO2poses for freshwater organisms, especially fish. The objective of this study was to determine how CO2may influence the growth rate, metabolic rate, feeding rate, and volitional behaviour of young-of-year Arctic charr ( Salvelinus alpinus (Linnaeus, 1758)), brook charr ( Salvelinus fontinalis (Mitchill, 1814)), and rainbow trout ( Oncorhynchus mykiss (Walbaum, 1792)). For this study, fish stayed in control (1100 microatmospheres (µatm)) or elevated (5236 µatm) CO2levels for 15 days. During this time, metabolic rate and behavioural tests were conducted on alternating days for each treatment. Weight and length of each fish were taken on days 0, 7, and 15. There was no evidence that elevated CO2affected the growth rate, feeding rate, or behaviour in any of these species. The standard metabolic rate in Arctic charr differed based on CO2exposure. Therefore, salmonids can withstand short periods of elevated CO2under these conditions. By comparing closely related species, the implications of this work are more ecologically relevant and will also help industry quantify the effects of high CO2on young salmonids.

Magneto-Mechanical and Thermal Properties of Nd-Fe-B-Epoxy-Bonded Composite Materials.

Polymer-bonded magnets are a class of composite material that combines the magnetic properties of metal particles and the molding possibility of a polymeric matrix. This class of materials has shown huge potential for various applications in industry and engineering. Traditional research in this field has so far mainly focused on mechanical, electrical or magnetic properties of the composite, or on particle size and distribution. This examination of synthesized Nd-Fe-B-epoxy composite materials includes the mutual comparison of impact toughness, fatigue, and the structural, thermal, dynamic-mechanical, and magnetic behavior of materials with different content of magnetic Nd-Fe-B particles, in a wide range from 5 to 95 wt.%. This paper tests the influence of the Nd-Fe-B content on impacting the toughness of the composite material, as this relationship has not been tested before. The results show that impact toughness decreases, while magnetic properties increase, along with increasing content of Nd-Fe-B. Based on the observed trends, selected samples have been analyzed in terms of crack growth rate behavior. Analysis of the fracture surface morphology reveals the formation of a stable and homogeneous composite material. The synthesis route, the applied methods of characterization and analysis, and the comparison of the obtained results can provide a composite material with optimum properties for a specific purpose.

Revisiting and redefining return rate for determination of the precise growth status of a species.

Growth curve models play an instrumental role in quantifying the growth of biological processes and have immense practical applications across all disciplines. The most popular growth metric to capture the species fitness is the "Relative Growth Rate" in this domain. The different growth laws, such as exponential, logistic, Gompertz, power, and generalized Gompertz or generalized logistic, can be characterized based on the monotonic behavior of the relative growth rate (RGR) to size or time. Thus, in this case, species fitness can be determined truly through RGR. However, in nature, RGR is often non-monotonic and specifically bell-shaped, especially in the situation when a species is adapting to a new environment [1]. In this case, species may experience with the same fitness (RGR) for two different time points. The species precise growth and maturity status cannot be determined from this RGR function. The instantaneous maturity rate (IMR), as proposed by [2], helps to determine the correct maturity status of the species. Nevertheless, the metric IMR suffers from severe drawbacks; (i) IMR is intractable for all non-integer values of a specific parameter. (ii) The measure depends on a model parameter. The mathematical expression of IMR possesses the term "carrying capacity" which is unknown to the experimenter. (iii) Note that for identifying the precise growth status of a species, it is also necessary to understand its response when the populations are deflected from their equilibrium position at carrying capacity. This is an established concept in population biology, popularly known as the return rate. However, IMR does not provide information on the species deflection rate at the steady state. Hence, we propose a new growth measure connected with the species return rate, termed the "reverse of relative of relative growth rate" (henceforth, RRRGR), which is treated as a proxy for the IMR, having similar mathematical properties. Finally, we introduce a stochastic RRRGR model for specifying precise species growth and status of maturity. We illustrate the model through numerical simulations and real fish data. We believe that this study would be helpful for fishery biologists in regulating the favorable conditions of growth so that the species can reach a steady state with optimum effort.

Effect of phosphate rock acid insoluble residue on hydration process and mechanical properties of α-hemihydrate gypsum

The application of α-hemihydrate gypsum (α-HH) is limited by several factors, such as a rapid hydration rate, short setting time, poor water resistance, and high cost. Especially because of the high production cost, although α-HH has excellent mechanical strength, it is rarely used in the field of building materials. In this study, based on the composition characteristics of new industrial solid waste (phosphate-rock acid-insoluble residue, PAIR) and to meet the needs of resource utilization, gypsum matrix composites were prepared by adding PAIR to α-HH to solve the problems of short setting time and poor water resistance of gypsum matrix composites and improve the comprehensive properties of α-HH products. The results show that when the different types of pores formed during the hydration of α-HH were filled with inert substances, such as silicon dioxide, insoluble phosphate, and calcium fluoride from PAIR, the proportion of mesopores in the composite products increased, whereas that of harmful macropores decreased. The compressive and flexural softening coefficients of the PAIR/α-HH system with 23% PAIR were the highest at 57.25 and 60.125%, respectively, and the water resistance of the system was improved; when the content of PAIR reaches 35%, the strength of the composite products decreased from 58.125 to 43.8MPa. The HPO42- in PAIR partially replaces the SO42- ion in the dihydrate gypsum (DH) lattice to form a Ca(SO4, HPO4)•2H2O double salt, leading to the production of eutectic phosphorus. Soluble F-, Al3+, Mg2+, and phosphorus-containing substances in PAIR form a variety of complex ions in PAIR/α-HH aqueous solution, which are adsorbed onto the surface of the new DH phase; the crystal morphology changed from thick, long columns to clusters, thin rods, and plates, inhibiting the nucleation and growth of DH and changing its crystal growth rate and crystallization behavior. Therefore, the setting time of gypsum is prolonged; when 35% PAIR was added, the induced nucleation period of the PAIR/α-HH system was prolonged from 40 to 265min, and the final setting time was from 12 to 360min. By mixing solid waste PAIR, while the setting time of α-HH is prolonged, its water resistance is improved, and its mechanical strength is not significantly reduced, reducing the cost. From the perspective of economy and environmental protection, this study is a way to α-HH is widely used in the field of building materials.

A robust probabilistic fatigue crack growth model based on walker’s crack growth rate equation for metallic materials

The fatigue crack growth data inherits statistical variation despite carefully controlled test procedures. The available probabilistic models rely extensively on fatigue crack growth test data of the coupon material under replicate loading conditions. In view of the often unavailability of such a database, this work proposes a new probabilistic model based on Walker’s crack growth rate equation and considers the variability in both the stress intensity factor range, ΔK and stress ratio, R. The optimum estimates of the model parameters are established using the maximum likelihood estimation (MLE) method. The model is examined using selected sets of measured fatigue crack growth curves of 7075-T6 and 2024-351 aluminum alloys. It demonstrates acceptable predictions for fatigue crack growth data on replicate and variable R-ratio loadings with failure probabilities in the range of 0.10 ≤pF≤ 0.90. The error on the observed fatigue crack growth rate data is normally distributed. The criterion of the minimum number of replicate tests for a valid probabilistic assessment of the fatigue crack growth data is established. Based on the mean squared error (MSE) parameter, the model provides a better representation of the mean fatigue crack growth rate behavior of the material for fatigue loading with variable R-ratios.