Corrosion wear models.
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More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
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Payan-Carreira",dateSubmitted:"April 21st 2020",dateReviewed:"September 10th 2020",datePrePublished:"October 8th 2020",datePublished:"January 20th 2021",book:{id:"8545",title:"Animal Reproduction in Veterinary Medicine",subtitle:null,fullTitle:"Animal Reproduction in Veterinary Medicine",slug:"animal-reproduction-in-veterinary-medicine",publishedDate:"January 20th 2021",bookSignature:"Faruk Aral, Rita Payan-Carreira and Miguel Quaresma",coverURL:"https://cdn.intechopen.com/books/images_new/8545.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"25600",title:"Prof.",name:"Faruk",middleName:null,surname:"Aral",slug:"faruk-aral",fullName:"Faruk Aral"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"38652",title:"Dr.",name:"Rita",middleName:null,surname:"Payan-Carreira",fullName:"Rita Payan-Carreira",slug:"rita-payan-carreira",email:"rtpayan@gmail.com",position:null,institution:{name:"University of Évora",institutionURL:null,country:{name:"Portugal"}}},{id:"309250",title:"Dr.",name:"Miguel",middleName:null,surname:"Quaresma",fullName:"Miguel Quaresma",slug:"miguel-quaresma",email:"miguelq@utad.pt",position:null,institution:{name:"University of Trás-os-Montes and Alto Douro",institutionURL:null,country:{name:"Portugal"}}}]}},chapter:{id:"73504",slug:"calf-sex-influence-in-bovine-milk-production",signatures:"Miguel Quaresma and R. Payan-Carreira",dateSubmitted:"April 21st 2020",dateReviewed:"September 10th 2020",datePrePublished:"October 8th 2020",datePublished:"January 20th 2021",book:{id:"8545",title:"Animal Reproduction in Veterinary Medicine",subtitle:null,fullTitle:"Animal Reproduction in Veterinary Medicine",slug:"animal-reproduction-in-veterinary-medicine",publishedDate:"January 20th 2021",bookSignature:"Faruk Aral, Rita Payan-Carreira and Miguel Quaresma",coverURL:"https://cdn.intechopen.com/books/images_new/8545.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"25600",title:"Prof.",name:"Faruk",middleName:null,surname:"Aral",slug:"faruk-aral",fullName:"Faruk Aral"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"38652",title:"Dr.",name:"Rita",middleName:null,surname:"Payan-Carreira",fullName:"Rita Payan-Carreira",slug:"rita-payan-carreira",email:"rtpayan@gmail.com",position:null,institution:{name:"University of Évora",institutionURL:null,country:{name:"Portugal"}}},{id:"309250",title:"Dr.",name:"Miguel",middleName:null,surname:"Quaresma",fullName:"Miguel Quaresma",slug:"miguel-quaresma",email:"miguelq@utad.pt",position:null,institution:{name:"University of Trás-os-Montes and Alto Douro",institutionURL:null,country:{name:"Portugal"}}}]},book:{id:"8545",title:"Animal Reproduction in Veterinary Medicine",subtitle:null,fullTitle:"Animal Reproduction in Veterinary Medicine",slug:"animal-reproduction-in-veterinary-medicine",publishedDate:"January 20th 2021",bookSignature:"Faruk Aral, Rita Payan-Carreira and Miguel Quaresma",coverURL:"https://cdn.intechopen.com/books/images_new/8545.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"25600",title:"Prof.",name:"Faruk",middleName:null,surname:"Aral",slug:"faruk-aral",fullName:"Faruk Aral"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}}},ofsBook:{item:{type:"book",id:"10648",leadTitle:null,title:"Vibrios",subtitle:null,reviewType:"peer-reviewed",abstract:"
\r\n\tVibrio is a genus of bacteria widely distributed in various aquatic and marine habitats. Among more than 100 species described, about 12 species can cause human infection, while others can cause marine animal infection. In order to guide the effective prevention and treatment of Vibrio infection, it is vital to have a deeper understanding of the pathogenic mechanism of Vibrio infection. At present, the potential molecular mechanism of vibriosis remains to be elucidated. The interaction among Vibrio, host and its host microbiota is an extremely complex biological process, all of which actively promote the balance between pathogenesis and clearance, which may affect the pathogenicity and host immune response and needs further study.
\r\n\r\n\tThe aim of this book is to introduce the current state of knowledge in the exciting and rapidly developing field of Vibrio virulence regulation and host interactions, especially the mechanisms involved in the cellular and molecular biological events that occur when host cells and pathogens interact in the harsh environment of an infected person/animal.
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An expert in investigating the molecular interactions of pathogens Vibrio alginolyticus with their hosts.",coeditorOneBiosketch:"An Associate Professor Fellow at the Yellow Sea Fisheries Research Institute, Chinese Academy of Fishery Sciences, a member of the China Society of Fisheries (CSF) and an expert in marine fish epidemiology and immunology with bacteria pathogen",coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"333148",title:"Dr.",name:"Lixing",middleName:null,surname:"Huang",slug:"lixing-huang",fullName:"Lixing Huang",profilePictureURL:"https://mts.intechopen.com/storage/users/333148/images/system/333148.jpg",biography:"Dr. Lixing Huang is an associate professor at Jimei University. He is mainly engaged in the molecular mechanisms research on the bacterial pathogen-host interaction, including but not limited to: 1) Applying dual RNA-seq and dual iTRAQ approaches to complex infection settings comprising of bacterial pathogens, their hosts and the resident gut microbiota; 2) Interplay between host cell microRNAs / proteins and bacterial infection; 3) Impact of bacterial pathogens on host cell RNA metabolism; 4) Effect of bacterial non-coding RNAs / proteins on key host intracellular pathways; and 5) Nutritional immunity, the struggle for nutrient metals between hosts and pathogens. He is the author of more than 60 research articles. 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His research has been directed at the epidemiology and immunology research on the bacterial pathogen of farming fish, including but not limited to: 1) Fish disease control: Investigation on epidemic disease and disease control of farming fish; 2) Fish vaccine development: Development of attenuated vaccine, inactivated vaccine, Pilot production of inactivated vaccine; 3) Pathogenicity mechanisms of fish pathogen: Function and interaction of bacteria secretion system. He is the author of about 10 research articles. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3621",title:"Silver Nanoparticles",subtitle:null,isOpenForSubmission:!1,hash:null,slug:"silver-nanoparticles",bookSignature:"David Pozo Perez",coverURL:"https://cdn.intechopen.com/books/images_new/3621.jpg",editedByType:"Edited by",editors:[{id:"6667",title:"Dr.",name:"David",surname:"Pozo",slug:"david-pozo",fullName:"David Pozo"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"65680",title:"Endoplasmic Reticulum Stress during Mammalian Follicular Atresia",doi:"10.5772/intechopen.82687",slug:"endoplasmic-reticulum-stress-during-mammalian-follicular-atresia",body:'The endoplasmic reticulum plays several important roles in normal cellular physiology. Some functions include protein synthesis, folding, and distribution to the Golgi apparatus. Alterations in protein synthesis inside the endoplasmic reticulum have been related to the trigger of different programmed cell death routes such as necroptosis, apoptosis, autophagy, and paraptosis, with apoptosis being the most studied process.
The mammalian ovary is an excellent model to study the mechanisms of programmed cell death because 99% of the follicles, the functional units of the ovary, undergo degeneration through follicular atresia, which maintains intraovarian homeostasis. Follicular atresia involves the physiological elimination of most germinal cells (oocytes) before they are ovulated, both in fetal and reproductive lives.
The presence of different programmed cell death pathways in follicular atresia have recently been shown, and these can be directly related to endoplasmic reticulum signaling. In this chapter we describe evidences of the linkage between endoplasmic reticulum alterations and programmed cell death, with special emphasis on follicular atresia.
The mammalian ovary is a paired organ that is responsible for generating competent oocytes for successful fertilization and early embryonic development. To do this, these germinal cells need to mature within transient functional complexes called follicles. Follicles form for an oocyte surrounded by somatic cells. During reproductive life, follicles are continuously recruited into the pool of growing follicles and change their size, morphology, and physiology, leading to different stage classifications including primordial, primary, secondary, and antral (Figure 1).
Ovary of mouse. Follicles are in different stages of growth. Primordial (P), primary (head arrow), secondary (asterisk), and antral (A) follicles.
At birth, the ovaries contain a fixed number of nongrowing primordial follicles, characterized by an oocyte enclosed by flattened pre-granulosa cells. In primary follicles, the oocyte is surrounded by a monolayer of cubical granulosa cells. Secondary follicles are formed by two or more layers of granulosa cells. Antral follicles accumulate fluid and develop an antral cavity. The accumulation of fluid is useful for transporting nutrients and waste products.
Follicular growth is a continuous process that is under strict control by hormones, growth factors, cytokines, and environmental factors. Follicle-stimulating hormone (FSH), luteinizing hormone (LH), insulin-like growth factor (IGF)-I, and estradiol are the principal regulators of follicular growth. FSH, a gonadotropin secreted by the pituitary gland, together with estradiol and IGF-I, is responsible for stimulating follicular growth and maturation. Moreover, FSH, LH, and estradiol enhance IGF-I secretion [1]. Additionally, FSH stimulates granulosa cells to develop LH receptor sites. The main function of LH is stimulating ovulation.
Several follicles grow and undergo ovulation, releasing an oocyte that is available for fertilization, but the principal destiny of ovarian follicles is follicular atresia, which is a physiological process that eliminates more than 99% of the follicles. Follicular atresia can occur in all stages of follicular development and ensures that only healthy follicles that contain optimal quality oocytes will be ovulated. Follicular degeneration occurs by programmed cell death (PCD). Apoptosis is the main route of follicular atresia, but may not be the only process involved (Figure 2). Other forms of PCD such as autophagy and paraptosis may also participate in this process [2, 3, 4].
Transmission electron microscope images of granulosa cells in different programmed cell death pathways. (a) healthy granulosa cell, (b) apoptotic body with highly condensed chromatin (cc), (c) autophagic cell with autophagic vesicles (head arrow), and (d) paraptotic granulosa cell with endoplasmic reticulum swelling (asterisk). Bars (a–c) 500 nm, and (d) 2 μm.
The endoplasmic reticulum (ER) is the organelle that is responsible for the folding and maturation of both transmembrane proteins and proteins that follow the route of secretion. Protein folding is facilitated by chaperones and oxidoreductases including binding immunoglobulin protein/glucose-regulated protein 78-kDa (BiP/GRP78), calnexin, calreticulin, and protein disulfide isomerase (PDI). An increase of cellular translational activity is possible under both normal and altered conditions, causing an overload of accumulating misfolding or unfolded proteins inside the ER. During ER stress, damaged proteins need to be degraded, but there is a limited number of proteases in the ER, and thus misfolded proteins are ejected from the ER and returned to the cytoplasm to be ubiquitinated and degraded by the 26S proteasome. These events are collectively referred to as ER-associated degradation (ERAD) [5]. Also, ER stress triggers the unfolded protein response (UPR), which is orchestrated by three ER-resident UPR sensors, inositol-requiring kinase 1 (IRE1), protein kinase R-like endoplasmic reticulum kinase (PERK), and activating transcription factor 6 (ATF6) [6, 7].
The UPR establishes an adaptive program aimed at re-establishing ER homeostasis by increasing the folding capacity of the cell, reducing protein synthesis, and enhancing the clearance of abnormally folded proteins and damaged organelles.
The proteins PERK and IRE1α and β are important players during UPR because they undergo oligomerization and autophosphorylation due to their interactions with peptides and unfolded proteins [8, 9]. Additionally, IRE1 promotes the unconventional splicing of X-box binding protein 1 (XBP-1) mRNA and an unspecific decrease of mRNAs better known as regulated IRE1-dependent decay (RIDD) [10, 11]. Afterward, the protein XBP-1 is translocated to the nucleus to activate the transcription of chaperones and ERAD factors [12]. RIDD suppresses protein inflow by degrading the mRNA of proteins with signal peptides or proteins with transmembrane domains, and in this manner RIDD permits proteins that are incorrectly folded inside the ER to be folded correctly [10]. PERK phosphorylates eukaryotic translation initiation factor (eIF2a), which then accumulates on the cytosolic side and leads to the downregulation of translation and enhances the translation of Grp78 and the transcription factor ATF4 [13, 14]. It has been shown that during early mouse embryonic development, Grp78 suppresses ER stress and pro-apoptotic pathways via ER signaling [15]. ATF6 is regulated by proteolysis in the Golgi apparatus, allowing the N-terminal fragments to be translocated into the nucleus where they function as a transcription factor [16, 17]. The processing of both ATF6- and IRE1α-mediated splicing of XBP1 mRNA is required for the full activation of the UPR [18].
UPR works like a protection mechanism. For example, in pancreatic beta cell line INS-1E, glucosamine and high glucose induce UPR activation and generate a feedback loop at the level of insulin transcription [19]. However, chronic or irreversible UPR can trigger cell death pathways, mainly apoptosis, but ER stress can induce other programmed cell death mechanisms including autophagy, necroptosis, and paraptosis.
Morphological ER disturbances during follicular atresia have been observed for a long time. Henderson et al. [20] observed a higher surface area of endoplasmic reticulum in granulosa cells cultured from atretic follicles. Moreover, researchers have used electron microscopy to observe the dilation and disintegration of RER cisterns and the swelling of mitochondria [21].
These morphological disturbances in ovaries are associated with ER stress and UPR activation under both physiological and pathological conditions [22]. UPR is present during follicular growth and maturation and follicular atresia and in the corpus luteum. ER stress during follicular growth and maturation has been evidenced by means of the expression of XPB1 and heat shock 70 kDa protein 5 (HSPA5) accompanied by the activation of IRE1 and PERK [23]. The ER stress level and cellular response depend on the signal and its intensity. It has been shown that a lipid-rich intrafollicular environment induces ER stress and impaired oocyte nuclear maturation [24]. Likewise, in the ovary a moderate activation of ER stress depends upon PERK and p38 signaling [25], evidencing a UPR response in the cells of this organ.
Apoptosis, the term proposed by Kerr et al. [26], describes an intrinsic suicide mechanism that involves cell shrinkage and the loss of cell contacts, chromatin condensation, and cleavage [27]. This process is better known as programmed cell death type 1 (PCD type 1). The biochemical activation of apoptosis can be directed through extrinsic and intrinsic pathways. The extrinsic pathway is initiated by the activation of cell surface death receptors to their ligands, like the Fas Ligand and TNF. After binding, apoptotic signals are transmitted through dead effector domains and caspase recruitment domains. The intrinsic pathway is governed by a variety of cellular stresses including DNA damage, endoplasmic reticulum stress, and nutrient deprivation, which culminates in mitochondrial outer membrane permeabilization (MOMP), resulting in the release of mitochondrial proteins including cytochrome c and Smac/DIABLO. Apoptosis pathways converge on a common machinery of cell destruction that is activated by caspases, a family of cysteine proteases that cleave after an aspartate residue [28, 29]. The caspases implicated in apoptosis are divided into initiators and executioners, where initiator caspases (caspase-8 and caspase-9) activate the executor caspases (caspase-3, caspase-6, and caspase-7).
The Bcl-2 family, which are central regulators of MOMP, are a large class of both pro- and anti-apoptotic proteins. The Bcl-2 family is divided into three subfamilies: multidomain anti-apoptotic such as BCL-2, BCL-XL (BCL2L1), MCL-1, BCL-W (BCL2L2), and A1 (BCL2A1), multidomain pro-apoptotic such as BAX and BAK, and pro-apoptotic BH3-only molecules that include BID, BIM, PUMA (p53 upregulated modulator of apoptosis), and NOXA [30]. BH3-only proteins antagonize anti-apoptotic BCL-2 proteins to release and activate Bak/Bax [31]. Bax and Bak induce external membrane mitochondrial permeabilization and cytochrome c release [32]. Nevertheless, some death stimuli can trigger caspase-independent cell death pathways where other organelles such as the endoplasmic reticulum and the mitochondria have an important function in the release and activation of death factors [33].
In atretic follicles, this PCD was thoroughly described by Tilly et al. [34] and can be conducted through the intrinsic or the extrinsic pathway [35]. In ovaries, apoptosis can be triggered by deprivation of various signal molecules, survival factors, growth factors (IGF and EGF), and gonadotropins (FSH and LH). Apoptosis can occur in both oocytes and somatic cells. Cell elimination has been observed in follicles in different stages of development, from fetal to adult organisms [3, 36, 37, 38]. Although different routes of PCD can occur during follicular atresia, apoptosis plays a major role (Figure 2b).
Apoptosis is triggered by chronic or irreversible ER stress and UPR and occurs through either the extrinsic or intrinsic pathway. Further, apoptosis can be carried out by two pathways, a classical Bax-/Bak-dependent apoptotic response that can be inhibited by ERK1/2 signaling and an alternative ERK1-/2- and Bax-/Bak-independent pathway [39]. No single component is entirely necessary, but the interaction of many different mechanisms results in apoptosis during ER stress [40]. Under ER stress Bax and Bak interact with the cytosolic region of IRE1α, which is required for the modulation of IRE1α signaling [41].
The activity of the BH3-only protein Bim is induced through different pathways. The first one involves protein phosphatase 2A-mediated dephosphorylation, which prevents its ubiquitination and the proteasomal degradation of Bim. A second pathway is direct transcriptional induction that is C/EBP homologous protein (CHOP)-C/EBPalpha-mediated, and a third comprises a repression of miRNAs led by PERK [42, 43]. On the other hand, PUMA, p53, and NOXA contribute to ER stress-induced apoptosis [44].
It has been reported that CHOP (a transcription factor of pro-apoptotic proteins such as Bim) increases during ER stress [45]. ATF4 and CHOP increase a generalized protein synthesis, provoking ATP depletion, oxidative stress, and cell death [46]. Also, IRE1α degrades the miRNA that represses caspase-2 mRNA translation, which causes an increase in the protein levels of this initiator protease of the mitochondrial apoptotic pathway [47].
ER stress and UPR during follicular atresia are not fully understood; however, there are several evidences of these processes in the ovary. For example, cisplatin, a widely used chemotherapeutic agent, can induce ER stress, which promotes apoptosis and autophagy in granulosa cells, causing excessive follicle loss and endocrine disorders [48].
In goat ovaries, ER stress is involved in follicular atresia through ATF6 and PERK/eIF2α/ATF4 signaling. Furthermore CHOP, caspase-12, and Grp78 proteins are upregulated in apoptotic granulosa cells during follicular atresia [49, 50]. ATF6 is a protein that is extensively distributed in the granulosa cells of ovarian follicles and oocytes in adult mice, and the amount of ATF6 increases in the presence of FSH and LH. ATF6 regulates apoptosis, the cell cycle, steroid hormone synthesis, and other modulators of folliculogenesis in granulosa cells, which may impact the development, ovulation, and atresia of ovarian follicles [51].
The presence of apoptosis-inducing factor (AIF) has been identified in granulosa cells. This protein mediates caspase-independent apoptosis and causes chromatin condensation and DNA fragmentation. AIF expression increases during follicular atresia, and AIF depletion protects ER stress-mediated goat granulosa cell apoptosis [52].
Reactive oxygen species (ROS) generation and oxidative stress can be upstream or downstream UPR targets. That is, UPR is interconnected with different enzymatic mechanisms of ROS generation, and they may depend on Ca2+ levels, ROS themselves, and PDI, which associates with NADPH oxidase and regulates its function [53]. ROS are pro-apoptotic factors in antral follicles. During oxidative stress, JNK activates FoxO1, which increases PUMA and induces apoptosis in granulosa cells [54]. Furthermore, pentosidine, a biomarker for advanced glycation end products, is accumulated in apoptotic human oocytes and increases with age [55].
UPR and ER stresses also have important roles in the regulation of corpus luteum (CL) regression. The overexpression of p-JNK, CHOP, caspase-12, and active caspase-3 during CL regression points to ER stress-dependent apoptosis [56, 57].
Autophagy is a catabolic pathway of cell constituents that contributes to cell survival in response to stress. Autophagy does not cause a loss of cell chemical components because the cell reutilizes them. There are three major types of autophagy, microautophagy, chaperon-mediated autophagy, and macroautophagy.
In microautophagy, vesicles bud into the lysosomal lumen by direct invagination of the boundary membrane, resulting in degradation of both cytoplasmic components and the lysosomal membrane by lysosomal hydrolases. This process involves sequential stages of vacuole invagination and vesicle scission [58].
Chaperon-mediated autophagy is the selective transport of proteins into lysosomes. The first step is protein recognition and lysosomal targeting. Protein recognition takes place in the cytosol through the binding of hsc70 to a KFERQ-like motif present in all chaperon-mediated autophagy substrates [59]. In the second step, proteins bind to receptors at the lysosomal membrane, Lamp2A, or a similar protein receptor for subsequent translocation and lysosomal degradation [60]. Receptors are subcompartmentalized in lipid microdomains to engage the processes of degradation, multimerization, and membrane retrieval [61].
Macroautophagy, also referred to as autophagy, involves the engulfment of cytoplasmic portions in a nonselective manner, as well as the degradation of specific proteins, organelles, and invading bacteria by a selective autophagy. Autophagy begins with the formation of an isolation membrane, the phagophore, which is a disk-like structure where the Atg machinery assembles. An isolation membrane grows to generate a double-membrane autophagosome, followed by elongation to form a mature autophagosome that captures cytosolic cargo. The fusion of mature autophagosomes with endosomes or lysosomes results in a single-membrane autolysosome where cargo is degraded by acid hydrolases [62].
Autophagy (Atg)-related proteins are the core machinery for autophagosome biogenesis and consist of several functional units: the ULK1-Atg13-FIP200-Atg101 protein kinase complex; the PI3K class III complex containing the core proteins VPS34, VPS15, and beclin 1; the PI3P-binding WIPI/Atg18-Atg2 complex; Atg9A; and the ubiquitin-like Atg5/Atg12 and Atg8/LC3 conjugation systems [63].
Autophagosome maturation involves the clearance of PI3P by Ymr1, a PI3P phosphatase, triggering the dissociation of the Atg machinery. Mature autophagosomes are transported to lysosomes through the microtubule cytoskeleton. The FYVE and coiled-coil domain containing 1 (FYCO1) protein binds to LC3, PI3P, and the small GTPase Rab7 and acts as an adaptor between autophagosomes and microtubules [64, 65]. Finally, the autolysosome is generated by autophagosome and lysosome fusion, where sequestered cargos are digested.
Autophagy and ER stress can be physiological processes in organisms. For example, they regulate endometrial function by modulating the mTOR pathway [66]. Also, autophagy contributes to the recovery of cell homeostasis after ER stress. During ER stress, damaged proteins are degraded by ERAD. However, some misfolded proteins are resistant, so autophagy is a final cell protection strategy deployed against ER-accumulated cytotoxic aggregates that cannot be removed by ERAD [67]. Additionally, ubiquitin is a common signal for both the ubiquitin-proteasome system and autophagy. In the mouse neuroblastoma cell line neuro-2a treated with tunicamycin, an ER stress inductor, the proteins involved in proteasomal degradation were downregulated, while proteins involved in ubiquitination were upregulated. Moreover, tunicamycin triggered autophagy, suggesting that it may serve as a compensatory effect to proteasomal degradation [68]. Also, ER-resident chaperones and enzymes that reduce the overload of misfolded proteins need to be removed by autophagy.
The structure or phagophore assembly site (PAS) localizes proximal to the ER. Autophagosome formation and transport to the vacuole are stimulated in an Atg protein-dependent manner. ER stress can induce an autophagic response because it increases Atg1 kinase activity and reflects both the nutritional status and autophagic state of the cell [69]. ER exit sites are essential for autophagy and are proximal to the PAS. Sec62, a constituent of the translocon complex that regulates protein import into the mammalian ER, intervenes during recovery from ER stress to selectively deliver ER components to the autolysosomal system for clearance and therefore is a critical molecular component in the maintenance and recovery of ER homeostasis [70].
The eIF2α/ATF4 pathway directs an autophagy gene transcriptional program in response to amino acid starvation or ER stress. The eIF2α kinase and the transcriptional factors ATF4 and CHOP are required to increase the transcription of a set of genes implicated in the formation, elongation, and function of the autophagosome, including Atgs and beclin 1, increasing the capacity to maintain autophagy in stressed cells. These autophagy genes exhibit different dependencies on ATF4 and CHOP, which means that they have a differential transcriptional response according to the stress intensity [71]. In human heart failure, the overexpression of the ER stress markers Grp78, PERK, CHOP, and ATF3 correlates with the expression of autophagy genes [72].
IRE1, a UPR sensor, has two isoforms, IRE1α and IRE1β, which both have RNase and kinase activities. However, in Arabidopsis thaliana, RNase activity of IRE1β, but not its protein kinase activity, is required for ER stress-mediated autophagy [73]. In Dictyostelium, the response to ER stress involves the combined activation of an IRE1α-dependent gene expression program and the autophagy pathway [74]. In mammalian cells, the spliced form of XBP 1 upregulates Nedd4-2, an E3 ubiquitin ligase involved in targeting proteins for subsequent degradation, in response to ER stress. It is also important for the induction of an appropriate autophagic response [75].
Different cancer cell models have allowed a better understanding of the mechanisms involved in autophagy triggered by ER stress. In cervical tumor cells, ER stress and UPR induced by X-ray exposition led to the activation of the NF-κB signaling pathway, autophagy, and apoptosis [76]. NF-κB is important for the proliferation, invasion, and metastasis of cervical cancer cells. Furthermore, in a model of breast cancer, autophagy and apoptosis were triggered through ER stress, UPR, and a high expression of CHOP and JNK [77].
Moreover, ERK and JNK activation is associated with cross talk between autophagy and another PCD. In L929 fibrosarcoma cells, ERK and JNK can link a signal from caspase-8 inhibition to autophagy, which in turn induce ROS production and PARP activation, leading to ATP depletion and necroptosis [78].
Ca2+ exchange between the ER and mitochondria is mediated through domains called mitochondria-associated membranes (MAMs). The interruption of Ca2+ flux between these organelles generates metabolic stress where AMPK present in MAMs triggers autophagy via beclin-1 phosphorylation [79, 80]. Autophagy activation might prevent proper interorganelle communication that would maintain mitochondrial function and cellular homeostasis [79].
In ER stress, some miRNAs promote the survival of the cells, while others promote cell death. In HeLa cells under RE stress, miR-346 positively regulates the expression of glycogen synthase kinase 3 beta (GSK3B) which reduces the interaction of beclin-1 and BCL2 to induce autophagy, ROS reduction, and cell death [81].
Autophagy is mainly induced in granulosa cells (Figure 2c) during folliculogenesis and shows a high correlation with apoptosis, and furthermore, both routes of PCD could play active roles in oocyte depletion [82]. According to Meng et al. [83], antral follicular degeneration is initiated by granulosa cell apoptosis, while preantral follicular atresia occurs mainly via enhanced granulosa cell autophagy. Surprisingly, apoptosis and autophagy can be present in the same cell at the same time, just as cells can show caspase-3 active, DNA fragmentation, and immunodetection of LC3 and Lamp 1 [2, 3].
The signals that establish autophagy or apoptosis as the route of cell death are not fully understood. Consistent with Zhang et al. [84], atresia initiation is associated with a cross talk of different PCDs including apoptosis and autophagy, a dramatic shift of steroidogenic enzymes, deficient glutathione metabolism, and vascular degeneration. In a rat model, FSH, a survival factor, decreased autophagy through LC3-II inhibition and Akt-mTOR pathway activation [85]. Shen et al. [86] assessed the mechanism involved in autophagy inhibition by the Akt-mTOR pathway in granulosa cells exposed to FSH and oxidative stress because mTOR, a negative regulator of autophagy, inhibits FOXO1, which promotes the expression of several autophagy genes. They found that FSH induced granulosa cell survival via FOXO1 inhibition by the PI3K-Akt-mTOR pathway [86]. Nevertheless, in mouse granulosa cells, FSH was related to follicle development and atresia because FSH induces autophagy signaling via HIF-1α [87].
Despite the studies on the role of the ER in autophagy, its specific participation in follicular atresia is still unknown.
Necroptosis is a subtype of regulated necrosis and shares the same morphological changes, including organelle swelling and membrane rupture. Necroptosis is a caspase-independent cell death, and its execution involves the active disintegration of mitochondrial, lysosomal, and plasma membranes. This PCD is triggered by various stimuli, such as TNF, Fas ligand, and TRAIL and depends on the serine/threonine kinase activity of RIP1. Additionally, a set of 432 genes regulates necroptosis and cellular sensitivity to this PCD by a signaling network that mediates innate immunity [88]. Moreover, Bmf, a BH3-only protein, is required for death receptor-induced necroptosis [88].
Moreover, environmental toxicants like cadmium can activate necroptosis. Intermediate levels of cadmium are associated with lost plasma membrane integrity, a decrease of ATP levels, and mitochondrial membrane potential and cell swelling, which are features associated with necroptotic cell death [89].
The core pathway of necroptosis relies on the assembly of an amyloid-like structure termed the necrosome. The necrosome is a multiprotein complex formed by receptor-interacting protein kinase 3 (RIPK3), RIPK1, and mixed lineage kinase domain-like (MLKL). Oligomerization and intramolecular autophosphorylation of RIPK3 lead to the recruitment and phosphorylation of MLKL. RIPK3 and MLKL continuously shuttle between the nucleus and the cytoplasm, whereas RIPK1 is constitutively present in both compartments [90]. Nuclear RIPK1 becomes ubiquitinated, and then nuclear MLKL becomes phosphorylated and oligomerized [90]. MLKL mediates plasma membrane rupture. MLKL forms cation channels that are preferentially permeable to Mg2+ in the presence of Na+ and K+ [91]. MLKL-induced membrane depolarization and cell death exhibit a positive correlation to channel activity.
The role of the ER in necroptosis has been evidenced using necrostatin-1, an inhibitor of necroptosis, which has a protective effect on the endoplasmic reticulum and mitochondria and alleviates ER stress after spinal cord injury [92]. Furthermore, Grp78 promotes an inflammatory response through the upregulation of necroptosis and subsequent activation of NF-κB and AP-1 pathways [93]. The depletion of reticulocalbin 1, an ER-resident Ca2+-binding protein, induces Grp78, activates PERK, and phosphorylates eIF2α. Moreover, the activation of CaMKII and the inactivation of Akt are important for necroptosis in response to reticulocalbin 1 depletion [94].
The function of MLKL and RIPK in necroptosis has been widely studied. The signal transducer and activator of transcription 3 (STAT3) was demonstrated to be downstream of calpain and regulates RIPK3 expression and MLKL phosphorylation and induces ER stress and mitochondrial calcium dysregulation [95]. Moreover, in cardiomyocytes upregulated RIPK1 and RIPK3 evoke ER stress, accompanied by an increase in intracellular Ca2+ levels and xanthine oxidase expression, which raised cellular ROS that mediated the mitochondrial permeability transition pore opening and necroptosis [96, 97]. In addition, the activation of JNK1/2 is regulated by RIPK3 [96].
Moreover, there are proteins that can participate in necroptosis and other types of PCD such as AIF and MLKL. Apoptosis-inducing factor (AIF), a protein normally located within the intermembrane space of mitochondria, is linked to apoptosis and necrosis. However, it has been shown that mitochondrial depolarization induced by ER stress promotes AIF release and nuclear condensation, which is consistent with necroptotic cell death [98, 99, 100]. MLKL, a member of the necrosome, also participates in chelerythrine (CHE)-promoted apoptosis through nuclear MLKL translocation and a special band of MLKL, which is promoted by a mutual regulation between the MLKL and PERK-eIF2α pathways in response to ROS formation [101].
Necroptosis has been widely researched, but there is still much to investigate, including the mechanism that mediates its execution. Nevertheless, necroptosis studies have been carried out under pathological conditions, and thus it is important to use physiological models like follicular atresia.
Necroptosis contributes to follicular atresia and luteolysis [102]. The factors involved in granulosa cell necroptosis can be regulated by acetylcholinesterase (AChE), cytokines, starvation, and oxidative stress via TNFα [103]. Also, an ovarian AChE variant, the read-through isoform AChE-R, has a nonenzymatic function that stimulates RIPK1-/MLKL-dependent necroptosis [103]. Therefore, although the participation of the ER in necroptosis and the contribution of this PCD in follicular atresia have been shown, the interrelation between ER stress-induced necroptosis and follicular atresia is completely unknown.
Sperandio et al. [104] introduced the term paraptosis to describe a route of caspase-independent PCD that has morphological, biochemical, and transcriptional features that are different from apoptosis [104]. Endoplasmic reticulum swelling, mitochondrial swelling, and resistance to apoptosis inhibitors without nuclear shrinkage or pyknosis characterize paraptosis. Although paraptosis is a caspase-independent cell death, participation of caspase-9 has been shown under experimental conditions [104].
Paraptosis can be triggered by different stimuli including insulin-like growth factor I receptor (IGFIR), JAY/TROY, and ROS. IGF-I is a regulator of multiple cell signaling pathways including PI3K-Akt1-RPS6 and ERK1/2 MAPK that are critical for cell proliferation, migration, and survival [105]. IGFIR-induced paraptosis is mediated by caspase-9, and at least two signal transduction pathways participate in the execution of paraptosis, the MAPK and JNK pathways [104, 106].
TAJ/TROY, a member of the tumor necrosis factor receptor superfamily, induces morphological features of paraptosis accompanied by phosphatidylserine externalization, the loss of the mitochondrial transmembrane potential, and independent caspase activation [105]. Moreover, programmed cell death 5 (PDCD5), an apoptosis-promoting protein, enhances TAJ-/TROY-induced paraptotic cell death [107].
ROS production can trigger paraptosis through PINK and mitophagy activation [108, 109]. Covalent modifications of free sulfhydryl groups on proteins cause protein misfolding and the accumulation of misfolded proteins, leading to ER stress, CHOP activation, and paraptosis [110, 111]. In malignant hepatoma cells with Bcl-xL-mediated apoptotic defects, the disruption of thiol homeostasis and treatment with doxorubicin and pyrrolidine dithiocarbamate induced paraptotic cell death [112].
The full signal transduction pathway and identification of specific markers for paraptosis are still unclear. Nevertheless, phosphatidylethanolamine-binding protein (PEBP-1), a suppressor of the MAPK pathway, has been identified, and prohibitin, a mitochondrial protein, is a mediator of paraptosis [113]. Furthermore, the redistribution of α- and β-tubulin and tropomyosin has been observed in the early stages of paraptosis. Other characteristics of the paraptotic pathway involve alterations mainly in signal transduction proteins, mitochondrial proteins, and some metabolic proteins [113].
Cancer cells are the best model to study paraptosis because there can be apoptosis and/or autophagy resistance. In melanoma cells, the sustained activation of the IRE1α and ATF6 pathways driven by the MEK/ERK pathway avoids ER stress-induced apoptosis [114].
Different compounds for cancer treatment have shown paraptosis induction. For example, HeLa, A549, and PC-3 cells treated with celastrol induced vacuoles derived from the dilation of ER, a feature of apoptotic cell death; moreover, this was accompanied by autophagy and apoptosis. Furthermore, the ER swelling triggered by celastrol induced ER stress markers including Grp78, PERK, IRE, and CHOP and alterations to proteasome function that resulted in the accumulation of ubiquitinated protein [115, 116]. Moreover, paraptosis can be accelerated by pre-treatment with the proteasome inhibitor MG132 [117]. On the other hand, cyclosporine A treatment of cervical cancerous SiHa cells showed ER stress and UPR preceded by massive cytoplasmic vacuole formation that culminated in a paraptosis-like cell death [118]. Moreover, murine hepatoma 1c1c7 cells and the human non-small cell lung cancer A549 cell line exposed to a combination of photodamage and benzoporphyrin derivative result in ER swelling and paraptotic cell death [119].
For the pathways involved in paraptosis, ER vacuoles can be dependent on the PI3K/Akt signaling pathway [120]. Moreover, in BC3H1 myoblast cell lines exposed to yessotoxin, paraptosis was accompanied by cytoskeletal alterations and the activation of JNK/SAPK1 [121]. However, in acute lymphoblastic leukemia cells, everolimus, a mTOR inhibitor, showed that JNK signaling was not required for paraptotic cell death [122]. Paraptosis in epithelial ovarian cancer (EOC) cells treated with morusin was characterized by VDAC-mediated Ca2+ influx into mitochondria, and subsequent mitochondrial Ca2+ overload contributes to mitochondrial swelling and dysfunction, leading to the accumulation of ER stress markers, the generation of ROS, and the loss of mitochondrial membrane potential (Δψm) in EOC cells [123].
Knowledge of the role of paraptosis during follicular atresia is still limited. In Bombyx mori, apoptosis, autophagy, and paraptosis occur in the ovarian nurse cell cluster during late vitellogenesis, whereas middle vitellogenesis is exclusively characterized by the presence of paraptosis, preceding both apoptosis and autophagy [124]. In mammals, paraptosis was evidenced by ER swelling (Figure 2d) and CHOP immunodetection in granulosa cells during follicular atresia in adult Wistar rats [4].
The mechanisms involved in paraptosis during follicular atresia are still unknown. The paraptotic inductor IGFR might be related because it is implicated in follicular growth and selection [104, 125]. Moreover, IGF2R and the binding protein genes IGFBP5 and IGFBP6 are overexpressed in atretic follicles [126]. However, more studies on paraptosis during follicular atresia are necessary.
Endoplasmic reticulum stress is a strong signal that triggers different programmed cell death pathways. Interestingly, programmed cell death via endoplasmic reticulum stress is not exclusive to pathological or experimental conditions but is present in physiological processes like follicular atresia. However, the specific mechanisms and signals for choosing a particular cell death pathway are still unknown. In this way, research on the pathways and mechanisms involved in programmed cell death activated by endoplasmic reticulum stress are fundamental, particularly for follicular atresia, as this process ensures the ovulation of competent oocytes for fertilization.
This work was supported by PAPIIT IN225117 and PAPIIT IN227919.
The authors declare no conflict of interest.
In a number of industries, in particular in the chemical industry, axial and radial turbomachines (compressors, superchargers, gas turbine installations, pumps) operate under aggressive environments, as a result of which rotor blades and disks are subject to corrosion wear.
Pipelines of hydropower are subject to corrosion wear, as a result of which their service life is significantly reduced. The problem of corrosion is especially acute in nuclear energy. Pipelines are made of low-alloy pearlite-grade carbon steel with stainless steel cladding on the inner surface. We also note that all parts and assemblies of the main circulation pumps in contact with the coolant, industrial cooling water, and locking water are made of special steels that are resistant to corrosion.
The coolant of the first circuit of a nuclear reactor is not just pure water, but water with boric acid dissolved in it (H3BO3), which contributes to significant corrosion of metal in pipelines. Steam generators of nuclear plants are made of pipes clad with anticorrosive austenitic surfacing.
It should be emphasized that the influence of the stress-strain state on the rate of corrosion and erosion wear also becomes important. For example, a strain of 1% increases the rate of corrosion of silicon iron in a 0.01% solution of sulfuric acid by 53% compared with undeformed metal [1].
Stress corrosion cracking of metals was previously studied. This phenomenon takes place at certain critical (threshold) values of tension determined by the acting stresses and potential energy. Stresses less than critical have an effect on general corrosion without causing cracking.
The impellers of radial and axial turbomachines subjected to corrosion are usually thin-walled plates and shells. The problem of the durability of the elements of the impellers of turbomachines is the problem of the durability of plates and shells of a variable thickness over time, under the influence of an aggressive environment that has certain parameters (degree of chemical activity, temperature, flow rate, etc.), and the stress-strain state.
One of the first works in this direction was an article by Kornishin [2], in which a joint solution of the corrosion equation is considered, which is a linear dependence of the corrosion rate on stress and equations describing the stress-strain state of a shell of variable thickness. The system of joint equations describing the behavior of the shell in a corrosive medium is then solved in finite differences according to a two-layer explicit scheme with a time step.
To date, there are a number of semi-empirical models that approximate corrosion wear taking into account the stress state. In Table 1, a number of models used in the calculations are given [3].
Corrosion wear models.
Table 1 indicates: h is the depth of the wear layer; t is the time; σ and ε are stress and strain; T is the temperature; k, α, β, and γ are constants; and φ (t) are some functions.
The issues of corrosion wear of centrifugal fan elements were investigated in a number of works by Pukhliy and Semenenko [1, 4, 5].
Bimetallic structures are widely used in modern technology, in particular, in the manufacture of bimetallic elements in nuclear energy. These are, first of all, bimetallic pipelines, bends, etc. These elements are characterized by high strength, heat resistance, and corrosion resistance.
The structural elements of nuclear power units operate under complex loading conditions, in particular, under conditions of exposure to aggressive environments. In this regard, the determination of the time to destruction of structural elements (resource) is the most important in the study of corrosion wear of elements that are in a complex stress-strain state [6, 7, 8].
In the present paper, an analytical approach to determining the resource of structural elements of nuclear power units based on the theory of bimetallic shells, taking into account the stress-strain state and corrosion wear of the elements, is presented.
Consider a cylindrical bimetallic shell when exposed to a corrosive environment [4]. Such tasks are very important in relation to the design of pipelines of nuclear power plants (corrosion cracking).
The rate of change of thickness at a given point in the shell is taken in the form:
with the initial condition:
where x, y are the normal coordinates of the middle surface of the shell; T is the temperature; and σ is the function connecting the rate of change of the shell thickness with the stress state at a surface point.
Note that F is a known function whose form is determined from experiment and
We study the effect of the stress state on general corrosion under the assumption that the corrosion rate is a linear function of the stress intensity.
The equations of corrosion wear are written as follows:
Here
It is necessary to add the equations of the theory of bimetallic shells to Eq. (1) or (3). As a result, we obtain an unrelated problem of the theory of shells, in view of which it is possible to apply a finite-difference approximation in time to the solution of Eq. (3).
Thus, the algorithm for solving the initial-boundary-value problem is reduced to the joint solution of Eq. (3) under the initial conditions in Eq. (2) and the system of equations for bimetallic shells, in the general case of variable thickness under the corresponding boundary conditions. Moreover, at each time step from Eq. (3), we obtain numerical values of the thickness of the structural element, which are then used to construct spline functions [9]. Then the system of equations of bimetallic shells is solved, from the solution of which the values of
The criterion for terminating the step-by-step process is the following condition:
where
The resource of structural elements of nuclear power units as a whole is determined by the summation of time steps.
We obtain the equilibrium equation of the bimetallic shell on the basis of the Lagrange variational principle:
Here
We write an expression for the variation of potential energy:
where
Integration extends to the entire surface of the junction (Figure 1): from
System of curvilinear coordinates on an undeformed junction surface.
In the analysis, the following assumptions are used (Figure 1).
The curvilinear coordinate system coincides with the lines of the main curvatures. This coordinate system is a Gaussian coordinate system, it is orthogonal.
The position of the point that does not belong to the junction surface determines the coordinates of the z-distance normal to the point from the junction surface (+ if it is directed along the internal normal to the junction surface).
The movement of u and v in are the direction of the tangents to
Deformations of the junction surface are determined by relative elongations
Eq. (5) can be represented as follows:
Denote by:
Then the variation of the potential of external forces is equal to:
Substituting Eqs. (6) and (7) in Eq. (4) we obtain:
Here
The last four terms in Eq. (8) is the work of concentrated forces along the edges of the shell
From Eq. (8), we obtain the equilibrium equation and boundary conditions.
In the mechanics of a solid deformable body, equilibrium equations can be obtained by making up for the main vector and the main moment of all the forces acting on the element for the infinitely small element extracted from the shell under the influence of external and internal forces (Figure 2). Here, the equilibrium equations and boundary conditions are obtained from the variational Lagrange principle in Eq. (4).
Internal forces acting on the edge of the element.
Note that in the case of dynamics, it is necessary to apply the variational Hamilton-Ostrogradsky principle.
So, from the first integral of expression in Eq. (8), the first three equations of equilibrium follow:
From the expressions in Eqs. (9)–(10), two more equations follow:
The sixth equation is an identity expressing the equality of the moments of all forces acting on the element to zero relative to the axis normal to the surface of the element junction:
This equation was used to obtain Eq. (11).
The second and third integrals of expression in Eq. (8) give boundary conditions for the edges
We emphasize that if one of the lines of the main curvatures is closed, then the displacements along this line will be periodic functions.
We introduce the following notation (Figure 3): R is the radius of the surface of the junction of a cylindrical bimetallic shell; l is the shell length;
Element of cylindrical shell.
Relative deformations of a surface located at a distance z from the junction surface (Figure 4):
Deformation of surface junction shell.
Normal stresses according to Hooke’s law:
Power factors:
Here:
Equations of an infinitesimal element:
The problem of axisymmetric deformation of an elastic bimetallic cylindrical shell for any relations between thicknesses, different mechanical characteristics of the material of the layers, and arbitrary heating along the thickness and axial direction is described by the equation:
Consider the case:
Then the force factors are written as follows:
Here
In this case, instead of Eq. (13), we obtain the following equation:
The boundary conditions for bimetallic shells coincide with similar conditions for homogeneous shells.
So, for a hard-pressed edge we get:
For the free edge we have:
We write the solution of the homogeneous Eq. (13) in the following form:
For an infinitely long shell in solution in Eq. (15),
Then:
Here
Example 1. Consider a bimetallic cylindrical shell under the influence of internal pressure q and a corrosive medium (Figure 5).
Geometry and loads acting on an element of two-layer shell: 1—outer layer; 2—inner layer; qa—internal pressure.
In this case, the stress intensity is constant for all points of the shell and is equal to [5]:
Given Eq. (16), Eq. (3) takes the form:
with the initial condition:
The initial thickness
Eq. (17) with the initial condition Eq. (18) is integrated in quadratures:
In case
We note that Eq. (20) differs from linear equation
Let us determine the durability of a steel two-layer cylindrical shell with Rc = 80.0 cm;
Corrosion rate,
Given Eq. (3) we get:
The final value of the thickness of the shell
Substituting the values of the coefficients in Eq. (3), we find the durability T = 11.6 years. In conventional calculations, the durability is calculated by the formula:
In conclusion, it should be noted that in the general case it is necessary to solve the unrelated problem of the theory of shells [10, 11], when at each step of integration over time it is necessary to solve the problem of the stress-strain state of a bimetallic shell by a variable thickness, for which it is necessary to use methods of integrating partial equations derivatives [12, 13].
The impellers of centrifugal pumps subjected to corrosion are usually thin-walled plates and shells. The problem of the durability of the elements of the impellers of centrifugal pumps is the problem of the durability of the plates and shells of a variable thickness over time, under the influence of an aggressive environment with certain parameters (degree of chemical activity, temperature, flow rate, etc.), and the stress-strain state.
Figure 6 shows the layout of a centrifugal pump. Consider the durability of the working blades of centrifugal pumps, which are a trapezoidal shell of variable stiffness (Figure 7). The blade is subject to the combined action of centrifugal load and corrosion wear.
Scheme of centrifugal pump: 1—confuser; 2—impeller; 3—diffuser.
Geometry and coordinate system of centrifugal pump blade.
The rate of change of thickness at a given point of the blade is taken in the form of a functional relationship:
with the initial condition:
where x, y are the coordinates of the middle surface of the scapula; T is the temperature; and σ is the function connecting the rate of change of thickness with the stress state at a surface point. Function F should be determined from experiment.
Assuming that the rate of change in corrosion wear is a linear function of stress intensity, we write Eq. (21) in the form:
Eq. (23) must be supplemented with shell theory equations of variable thickness.
Omitting the intermediate calculations, we present a system of partial differential equations of the type Margherra [14] with respect to the normal deflection w and the stress function F of the eighth order, describing the stress state of the blade of variable thickness, taking into account the temperature effect:
Here T = T(x, y, z) is the temperature field of a general form; α is the coefficient of linear expansion of the material of the blade.
Power factors due to temperature exposure are recorded as:
We introduce the dimensionless coordinate system:
and dimensionless unknown functions
Here
The boundary conditions at the edges of the blade adjacent to the disks
The boundary conditions at the inlet and outlet edges of the blade correspond to the free edge. In this case we have:
The important issue is to specify the function of changing the blade thickness h = h (x, y) in the process of erosion-corrosion wear.
In our studies, the function of changing the blade thickness was set in the form of cubic splines [9].
In the general case, the blade thickness can be represented as two-dimensional spline interpolations:
This function on each element of the surface of the scapula
is a bicubic polynomial, continuous, and has continuous partial derivatives up to and including
We represent the system of Eq. (24) in a dimensionless form:
where
The analytical solution of the system of Eq. (31) with boundary conditions in Eq. (28) is based on the application of the method of integral relations by Dorodnitsyn [13].
In accordance with the method, we write the initial system of Eq. (31) in divergent form:
where
Through
In Eq. (32)
Following the method of integral relations of Dorodnitsyn [13], we look for a solution to the system of Eq. (32) in the form of an expansion:
As approximating and weighting functions, we choose the Jacobi system of orthogonal polynomials [15, 16] and their derivatives:
Here
Note that polynomials
We also emphasize that their derivatives
Restricting ourselves to the two-term approximation and also choosing power polynomials
It should be noted that in the general case there is no exact solution of such equations in mathematics, with the exception of individual special cases, for example, the Bessel equation.
Here, the modified method of successive approximations developed by Professor Pukhliy and published by him in the Academic Press [12, 17] is applied to the solution of the boundary-value problem.
Later, the method was extended to the solution of initial-boundary value problems [4], and to accelerate the convergence of the solution, the method of telescopic shift of the power series of K. Lanczos [18] was used. For this, we used the possibility of representing any power series in terms of shifted Chebyshev polynomials [15, 16]. For the first time, such an approach was presented in the works of V.A. Pukhliy [19, 20].
In accordance with the method, variable coefficients
Here q is the degree of the interpolation polynomial and
The general solution of the system of Eq. (34) has the form [10, 19, 20]:
where
The first approximation
Subsequent approximations are carried out according to the formulas:
The systems of fundamental functions in Eq. (37) are uniformly converging series, and the coefficients
The constants
Thus, the problem reduces to the joint solution of Eq. (23) and the system of Eq. (24) under initial conditions in Eq. (22) and boundary conditions in Eqs. (28) and (29). Moreover, at each time step, from Eq. (23) we obtain the numerical values of the thickness, which are used to construct spline functions in Eq. (30). Then the system of Eq. (24) is solved, from the solution of which the values
The criterion for terminating the step-by-step process is the condition:
where
The durability of the impeller element of centrifugal pumps is obtained by summing the steps in time.
The theory of corrosion wear of structural elements of hydropower and nuclear energy in the form of plates and shells is developed taking into account the stress state and corrosion wear.
Numerous factors affecting the speed of the corrosion wear process (degree of aggressiveness of the media, temperature, humidity, etc.) are taken into account in a generalized way by drawing up a differential equation for the rate of change of the thickness of the impeller element.
The criterion for the ultimate state of structural elements is the achievement by the structural element of the yield strength of the material
An algorithm has been developed for solving the problem of corrosion wear of bimetallic pipelines of nuclear energy, taking into account the stress-strain state of the elements.
An algorithm has been developed for the analytical solution of the problem of corrosion wear of rotor blades of centrifugal pumps based on a combination of the method of integral relations and the modified method of successive approximations in displaced Chebyshev polynomials.
Research has been funded by RFBR and City of Sevastopol under Research Project №18-48-920002.
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