Çok eksenli yorulma durumunda eşzamanlı ve asenkron yüklemeler için hasar ve ömür kestirim yöntemlerinin incelenmesi
Investigation of damage and life estimation methods for in-phase and out-of-phase loading in multiaxial fatigue
Yazar: BURAK UĞUR BULCA
Danışman: DR. ÖĞR. ÜYESİ OĞUZ ALTAY ; PROF. DR. ATA MUGAN
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Katı Cisimlerin Mekaniği Bilim Dalı
Derece: Yüksek Lisans, 2023
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Coffin-Manson Yöntemi = Coffin-Manson Method ; Gerilme dağılımı = Stress distribution ; Sonlu elemanlar yöntemi = Finite element method ; Yorulma = Fatigue

Özet:
Günümüzde, mühendislik alanında en çok karşılaşılan ve hasara sebebiyet veren problemlerin başında yorulma gelmektedir. Yorulma, tekrarlı veya değişken yüke maruz kalan yapıların hasara uğrama eğilimi olarak tanımlanabilir. Genellikle yorulma hasarı, malzemelerin akma dayanımlarının altında olan büyüklükteki yükler sebebiyle gerçekleşir. Tasarım yapılırken tekrarlı ya da değişken bir yükün varlığı, her zaman öncelikle yorulma etkisini göz önünde bulundurmayı gerektirir. Mühendisliğin faaliyet gösterdiği alanlara bakıldığında ise aslında birçok durumda yapıların bu tarz yüklere maruz kalması kaçınılmazdır. Sektörel olarak bakıldığında havacılık, otomotiv, denizcilik, demiryolu taşımacılığı ve inşaat sektörü gibi kısacası hayatın her alanında karşılaşılabilir olan bu durum, özellikle dönen ve güç aktarması gereken her türlü mekanizma ve yapının öncelikli problemi olmuştur. Bu problem yalnızca teknik açıdan değil, gerek maliyet düşürme odaklı tasarımların geliştirilmesi, daha hafif ve kullanımı kolay ürünlere olan ihtiyaç ve ortaya çıkabilecek muhtemel kusurlar dolayısıyla insan hayatını doğrudan etkileyebilecek bir öneme sahiptir. Bu sebeple tasarım süreçlerinde, parçanın fonksiyonel olarak kullanılacağı süre boyunca tekrarlı yüklere ne kadar ve hangi şiddette maruz kalacağı, bu parçanın ya da yapının ne kadarlık kullanım ömrüne ihtiyacının olduğu ve eğer gerekli ise düzenli bakım ve servis şartlarının nasıl olması gerektiğinin önceden belirlenmesi gerekmektedir.
Dönen ve güç aktaran yapıların maruz kaldıkları dış yükler, genellikle yapı üzerinde farklı yönde gerilmeler oluşturmaktadır. Tek eksenli yorulma deneyleriyle geliştirilmiş malzeme yorulma eğrileri ve çözüm yaklaşımları, bileşik gerilmeye maruz kalan yapıların ömür tahmini hesapları için yetersiz kalmaktadır. Özellikle yüklerin tesiri sırasında aralarında faz farkı bulunması yorulma hasarı hesaplarını oldukça zorlaştırmaktadır. Bu nedenle, çok eksenli yüklere maruz kalan yapıların ömür tahmini konusu özel bir konu olarak ele alınmaktadır.
Tezin temel amacı ise mevcut bileşik gerilme durumlarında ömür tahmin yaklaşımlarını incelemek, literatürdeki tamamlanmış deney verileri yardımıyla ticari yazılımlar kullanılarak eşzamanlı ve faz farklı yükleme durumlarında en doğru sonuç veren yaklaşımı tespit etmek ve ömür tahmin yöntemlerinin birbirlerine göre avantaj ve dezavantajlarını kıyaslayarak karşılaşılabilecek farklı problemler için takip edilebilir bir çözüm yöntemi sunmaktır.
Literatür araştırmasında, çok eksenli yorulma durumları için oldukça çeşitli ve geniş kaynaklar bulmak mümkündür. Bu yaklaşımlar birim şekil değiştirme bazlı, gerilme bazlı ya da enerji bazlı olacak şekilde sınıflandırılabilir. Yorulma konusunun karmaşık bir problem olmasından dolayı uzun yıllardır süren araştırmalar sonucunda net bir yargıya varılamamış olduğu gözükmektedir. Bu yaklaşımların yanı sıra bileşik gerilme durumunda malzeme davranışlarını daha detaylı inceleyen ve daha isabetli ömür tahmini yapılmasını sağlayan lokal plastisite yaklaşımları ve onların matematiksel modellerinden bahsedilmiş, karmaşık yükler için uygulanan Rainflow çevrim sayma yöntemi gösterilmiş ve toplam hasarın tespiti için kullanılan Miner-Palmgren kuralı açıklanmıştır.
Çalışma kapsamında, Prof. Dr. Jan Papuga'nın araştırmalarında yer alan deney verileri SolidWorks, Hypermesh, ABAQUS ve FEMFAT yazılımları yardımıyla bilgisayar ortamında modellenmiş ve farklı ömür tahmini yaklaşımlarıyla analiz edilmiştir. Ortalama gerilme değerinin sıfır olduğu senkron ve farklı faz açılarındaki asenkron yükleme sonuçları detaylıca incelenmiş, ayrıca ortalama gerilme varlığının yorulma ömrüne olan etkileri gerek senkron gerekse asenkron yükleme durumlarında karşılaştırılmıştır. FEMFAT yazılımı içerisinde, farklı bileşik gerilmeli yorulma durumları için kullanılan hesaplama yöntemleriyle elde edilen sonuçlar deney verileriyle kıyaslanmıştır. Yaklaşımların ömür tahmini sonuçları üzerinden metotların isabetliliği ile güçlü ve zayıf yanları gösterilmiştir. Son bölümde ise elde edilen sonuçlar hakkında genel yorumlar ile çalışmanın gelişime açık yanları ele alınmıştır.

Abstract:
Today, fatigue is one of the most common and damaging problems in engineering areas. Fatigue can be defined as the tendency of structures which are subjected to repeated or variable loads to initiate damage. Generally, these loads create stress which is below the yield strengths of the materials. During design process, the one of the most important parameters which must be into consideration is the presence of a repetitive or variable load which can be cause of fatigue failure. In engineering systems, it is inevitable for structures to be exposed to such loads in many cases.
Fatigue failures in engineering areas, which can be encountered in all areas of life such as aviation, automotive, maritime, railway transportation and construction, has become the primary problem of all kinds of mechanisms and structures that rotate and transmits power. This problem is not only important technically, but also has an importance that can directly affect human life due to possible failures which may arise. In addition, development of cost-reducing designs, the need for lighter and easier-to-use products can be counted as other reasons to prove importance of studies in the fatigue area. Therefore, during design processes, it is necessary to determine that how long and at which stress level the part will be exposed to repeated loads during the period of functional use, how long this part or structure will be required to maintain the functionality of the mechanism or structure, and if necessary, what should be frequency of regular maintenance and service conditions.
Rotating mechanisms and power-transmitting structures are exposed to external forces which are generally create stresses on the structure which is named as multiaxial loading. Material fatigue curves and fatigue life estimation approaches developed on uniaxial fatigue tests are insufficient for life estimation calculations of structures subjected to combined stresses. Especially depending on load timing, can be applied in-phase or out-of-phase, the phase angle between different load sources increases the complexity of fatigue life estimation calculation. Therefore, fatigue life estimation of structures which are subjected to multiaxial loads is considered as a special topic in solid mechanics.
The main purposes of the thesis is to examine the fatigue life estimation approaches in multiaxial loading, to determine the most accurate calculation approach in-phase and out-of-phase loading situations by using commercial software based on completed test results in the literature, and to compare the advantages and disadvantages of fatigue life estimation methods in multiaxial loading and to be able to select the most fitted fatigue life estimation method for different loading scenarios that may be encountered.
In the literature search, it is possible to find a wide variety of sources for multiaxial fatigue life estimation methods. These approaches include strain-based, stress-based or energy-based approaches. Due to the fact that the issue of multiaxial fatigue, especially in out-of-phase loading is a complex problem, it seems that a clear judgement could not be reached yet as a result of many years of research. The main reason for this is the existence of many factors that can cause multiaxial fatigue damage. Loads with variable amplitudes, presence of mean stress, timing of loads from different axes (in-phase loading or the case of loads acting with a certain phase difference which is named as out-of-phase loading), geometry of the studied structure, roughness of the material used, chemical components, thermal factors, etc. These parameters are the main reasons which make very complex fatigue life estimation in multiaxial loading.
In general, a three-step process is followed in the multiaxial fatigue life estimation of structures which are exposed random loading. These processes are the determination of equivalent stress in the critical plane and the stress cycles resulting from multiaxial loading by cycle counting methods, the damage calculation for each cycle separately, and finally the summation of the calculated damage values in order to evaluate total damage status.
Considering the out-of-phase loading scenarios, which are the main subject of this thesis, results were obtained within the low cycle number limits as observed in the experiments. For this reason, it has been observed that strain-based approaches give more accurate results. In addition to these, considering that local plastic deformation factors are also effective, so that is another reason to explain a strain-based approach in this topic.
It has been observed that in the literature search, most of multiaxial fatigue life estimation approaches use the critical plane approach to define the most critical section that expected crack initiation location. Critical plane is defined as the plane which has maximum strain range values. According to material structure and loading type, materials have different failure modes and critical plane approach provides to estimate shear-based failure mode location. In order to achieve that, strain tensor, defined based on general coordinate system, is transformed to every possible plane which has same origin point to be able to catch maximum strain range.
Considering all information, a strain-based method Manson-Coffin Equation is explained in detail which is based on critical plane approach, uses both effect of elastic and plastic strains, defines a ratio which named critical stress ratio and provides best selection of critical plane and gives better results for both in-phase and out-of-phase loading cases.
In addition to multiaxial fatigue life estimation approaches, local plasticity corrections such as Neuber correction, Glinka method and Ramberg-Osgood equation for cycling hardening theory which examine the material behavior in more detail in the case of multiaxial loading and provide more accurate results for fatigue life estimation are explained. Rainflow cycle counting method is also explained which is used to count hidden closed and half cycles in loading history for complex loadings. Finally, the Miner-Palmgren rule which is used for determining the total damage by summing damage results from each cycle that are defined by Rainflow counting is explained.
Within the scope of the study, the experimental data which has been taken from studies of Mr. Jan Papuga from Czech Technical University were modeled and analyzed in computer aided engineering softwares such as SolidWorks, Hypermesh, ABAQUS and FEMFAT.
Within the scope of multi-axial fatigue life estimation studies, experiment data were found from the experiment with bending and torsional loads in the literature. Then, the specimen used in these experiments was modeled as a solid body with the 3D design software SolidWorks, and static bending and static torsion analyses were completed under unit forces with the help of ABAQUS software. The resulting result files are defined in the FEMFAT software for defining the finite element model and transferring the stress tensors. Harmonic load curves were created in FEMFAT by considering the stress amplitude, mean stresses and phase angles performed in the test. The factors to be activated according to the relevant test scenario were determined, the survival probability was set to 50%, and the critical plane search parameters were determined. Experiments were selected especially including phase angle effect and also mean stress effect in order to understand the effects of different load scenarios on the total cycle life and also to be able to compare fatigue life estimation methods such as different conditions.
Firstly, the results of in-phase and out-of-phase loading with different phase angles has been examined and analyzed in detail, where the mean stress value is zero. The effects of mean stresses on the fatigue life have been investigated in both in-phase and out-of-phase loading conditions. The results obtained with the calculation methods used for different combined stress fatigue states in the FEMFAT software were compared with the experimental data. Also, each calculation approach has been explained in this study. The accuracy capability, strengths and weaknesses of the fatigue life estimation approaches in multiaxial loading are shown on the life estimation results.
For better evaluation of the analysis results, the fatigue curve of the relevant experiment was drawn by taking the average of the different life results determined for two different amplitude points with the help of the test. Error curves were created based on this data, and the error rates of the results were calculated based on these average values. Average cycle lives which are obtained in the test data and life cycle results from analysis with different methods, are compered on the tables. Also, for better representation of the results, dispersion of the test and analysis results is shown in graphs with error bands.
In the last part, general comments about the results obtained and the aspects of the study that are open to improvement are discussed. As mentioned in the literature, in case of multiaxial fatigue, the life of the structure decreases with the phase difference between the loads or the presence of the average stress effect. This situation was observed in the experiments and was determined by the analysis results.