Faculdade de Engenharia Mecânica
EDUARDO AUGUSTO BARROS DE MORAES
Numerical and Experimental Fatigue Analysis of
Crankshafts
Análise Numérica e Experimental de Fadiga de
Virabrequins
CAMPINAS
2017
Numerical and Experimental Fatigue Analysis of
Crankshafts
Análise Numérica e Experimental de Fadiga de
Virabrequins
Dissertation presented to the School of Me-chanical Engineering of the University of Campinas in partial fulfillment of the require-ments for the degree of Master, in the area of Solid Mechanics and Mechanical Design. Dissertação apresentada à Faculdade de Engen-haria Mecânica da Universidade Estadual de Campinas como parte dos requisitos exigidos para a obtenção do título de Mestre em Engen-haria Mecânica, na Área de Mecânica dos Sóli-dos e Projeto Mecânico.
Orientador: Prof. Dr. Marco Lucio Bittencourt
ESTE EXEMPLAR CORRESPONDE À VERSÃO FINAL DA DIS-SERTAÇÃO DEFENDIDA PELO ALUNO EDUARDO AUGUSTO BARROS DE MORAES, E ORIENTADA PELO PROF. DR. MARCO LUCIO BITTENCOURT.
CAMPINAS 2017
Ficha catalográfica
Universidade Estadual de Campinas Biblioteca da Área de Engenharia e Arquitetura
Luciana Pietrosanto Milla - CRB 8/8129
Moraes, Eduardo Augusto Barros de,
M791n MorNumerical and experimental fatigue analysis of crankshafts / Eduardo Augusto Barros de Moraes. – Campinas, SP : [s.n.], 2017.
MorOrientador: Marco Lúcio Bittencourt.
MorDissertação (mestrado) – Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica.
Mor1. Virabrequins. 2. Metais - Fadiga. 3. Automóveis - Testes. 4. Métodos numéricos. 5. Modelos de campo de fase. I. Bittencourt, Marco Lúcio,1964-. II. Universidade Estadual de Campinas. Faculdade de Engenharia Mecânica. III. Título.
Informações para Biblioteca Digital
Título em outro idioma: Análise numérica e experimental de fadiga de virabrequins Palavras-chave em inglês:
Crankshafts Metals - Fatigue Cars - Testing Numerical methods Phase field models
Área de concentração: Mecânica dos Sólidos e Projeto Mecânico Titulação: Mestre em Engenharia Mecânica
Banca examinadora:
Marco Lúcio Bittencourt [Orientador] Pablo Siqueira Meirelles
Heraldo Silva da Costa Mattos
Data de defesa: 31-07-2017
Programa de Pós-Graduação: Engenharia Mecânica
FACULDADE DE ENGENHARIA MECÂNICA
COMISSÃO DE PÓS-GRADUAÇÃO EM ENGENHARIA MECÂNICA
DEPARTAMENTO DE SISTEMAS INTEGRADOS
DISSERTAÇÃO DE MESTRADO ACADÊMICO
Numerical and Experimental Fatigue
Analysis of Crankshafts
Análise Numérica e Experimental de
Fadiga de Virabrequins
Autor: Eduardo Augusto Barros de Moraes Orientador: Prof. Dr. Marco Lucio Bittencourt
A Banca Examinadora composta pelos membros abaixo aprovou esta Dissertação:
Prof. Dr. Marco Lúcio Bittencourt FEM/UNICAMP
Prof. Dr. Pablo Siqueira Meirelles FEM/UNICAMP
Prof. Dr. Heraldo Silva da Costa Mattos Universidade Federal Fluminense/Niterói
A Ata da defesa com as respectivas assinaturas dos membros encontra-se no processo de vida acadêmica do aluno.
que sempre me apoiaram para alcançar meus sonhos, à minha esposa Julia, minha eterna companheira e ao meu filho Lucas, maior fonte de inspiração em minha vida.
Gostaria primeiramente de agradecer a Deus por todas as oportunidades, e por me dar apoio e forças nas horas mais difíceis.
Agradeço imensamente ao professor Marco Lúcio Bittencourt, que me deu a opor-tunidade de trabalhar neste projeto, pelos ensinamentos e lições que levarei por toda vida acadêmica. Agradeço também ao professor Paulo Roberto Zampieri por trabalhar em conjunto nos desenhos e dimensionamento das peças, e por sua grande sabedoria nos mais diversos as-suntos. Obrigado também ao professor Boldrini pelos grandes ensinamentos.
Em especial, gostaria de agradecer ao pessoal do Laboratório de Ensaios Dinâmi-cos, LabEDin. Sem vocês este trabalho não seria possível! Obrigado Vivan e Kazumi pelos en-sinamentos, Leo e Geraldo por todo o auxílio com usinagem e soldagem, Marcelo e Fábio por literalmente toda a força que vocês me deram nas montagens e Sérgio por todos os ensinamentos e auxílio na instrumentação das amostras. Fica aqui também meus sinceros agradecimentos ao Renan, que me ajudou nas partes mais críticas das montagens e agora irá continuar este legado. Agradeço aos professores Janito Vaqueiro Ferreira pelo auxílio e toda disposição durante o planejamento do experimento, e pelo empréstimo de equipamentos essenciais. Ao Fernando Ortolano, muito obrigado pela disposição com o setup do experimento e por toda a ajuda nas montagens. Gostaria de agradecer também ao professor Pablo Siqueira Meirelles pelas constantes lições ao longo deste tempo.
Agradeço também aos demais funcionários da FEM que auxiliaram este projeto. Maurício, pela fabricação das amostras, Zé Luis obrigado pelos testes de tração e fadiga, Clau-denete, obrigado pelo auxílio. Um agradecimento especial aos colegas Sérgio Villalva e Élcio Ferracini que tanto contribuiram no desenvolvimento do aparato experimental.
Agradecimentos ao professor Waldyr Luiz Ribeiro Gallo por gerenciar o projeto temático, à Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) pela concessão do auxílio à pesquisa e bolsa de mestrado e ao Grupo PSA do Brasil pelo apoio durante o projeto.
A todo o pessoal do lab, muito obrigado pela convivência, pelos churrascos e por gerarem um excelente clima de trabalho. Alfredo, obrigado pelo template em LATEX, e por
pro-porcionar as melhores histórias! Obrigado ao grupo de phase field, Luis, Fabiano e Geovane por todo aprendizado! Ao Guilherme e Beto e Jonatha pelo excelente convívio e Jonatha: valeu pela companhia durante as reuniões de projeto! À Darla e Mari pelas conversas. Ao Jorge agradeço imensamente a toda paciência em me ensinar muitas coisas que levarei comigo em minha vida profissional. Obrigado por todo apoio e convivência!
meu lado, desde o colégio. Obrigado Renan por ser um amigo pra todas as horas e pelos grandes momentos ao longo dos anos! Obrigado ao Thiagão por todo incentivo, por me ensinar muito e por ser uma referência desde a época de colégio. Aproveito para agradecer também seu pai Renato e tantos outros professores do colégio que me ensinaram muito mais do que o conteúdo. Ao meu compadre Kozuki, obrigado por esses 13 anos de convivência, risadas, piadas, e todo o resto que não cabe aqui. Valeu pessoal por fazer da Rep. Caipiroska a única Rep. possível!
Para que eu chegasse até aqui, o apoio da família toda foi indispensável. Não con-seguirei citar todos aqui, mas saibam que tenho todos no coração. Em especial, agradeço a meus pais, Eduardo e Ângela, por tudo que conquistei. Tudo que sou hoje, profissional e pessoalmente eu devo a vocês. Vocês confiaram e investiram em mim, me apoiaram em todos os momentos da minha vida, e são meus exemplos, meus modelos e inspiração diárias e espero sempre poder retribuir a vocês tudo que fizeram e ainda fazem por mim. Obrigado! Minha irmã Isabela, muito obrigado pela convivência, pelas risadas, pelas piadas sem graça que só nós dois entendemos e por todas as vezes que nós saímos pra comer comidas espetacularmente erradas! Agradeço por poder fazer parte desta família. Agradeço também ao meu sogro Vicente, minha sogra Eliane e minha comadre Bruna por todo o apoio esses anos todos.
Por último, deixo agradecimentos tão importantes, que são os mais difíceis de escr-ever. Julia, minha amiga, minha parceira, meu amor! Não existem palavras adequadas nem em um milhão de dicionários que consigam descrever o que sinto por você! Só consigo dizer muito obrigado! Obrigado pelo carinho, pelo apoio, por cuidar de mim nas horas mais difíceis, por me amparar todas as vezes que senti vontade de desistir de tudo, por batalhar todos os dias comigo nesse mundo tão complicado, por me ensinar muito e me direcionar para o melhor caminho sempre! Só nós sabemos o que passamos para chegar até aqui, e nós conseguimos e vamos con-tinuar em frente sempre juntos! Agradeço a você também pelo melhor presente que eu poderia ter na vida, nosso grande Lucas. Filho, obrigado por me inspirar, por me fazer querer ser melhor a cada dia, por me fazer entregar o máximo de mim para dar o melhor futuro para você! Você nos guia e nos inspira, com seu jeito, suas risadas e seu carinho. Julia e Lucas, obrigado por estarem do meu lado neste momento e por serem a minha família!
Os virabrequins estão sujeitos a cargas elevadas em motores de combustão interna, levando a ciclos de tensão de flexão e torção. Falha por fadiga é uma grande preocupação no design de virabrequins, sendo necessárias muitas horas de teste de fadiga, tornando o projeto caro e ex-tenso. Com o objetivo de reduzir custo e tempo de projeto, utilizamos o método de elementos finitos para estimar condições do teste e distribuição de tensões no virabrequim sob flexão. Nós verificamos a precisão do modelo comparando os resultados numéricos com dados experimen-tais obtidos por um aparato de teste de fadiga em flexão ressonante, que nós desenvolvemos e construímos. O aparato ressonante é usado para obter dados de fadiga de amostras de vira-brequins usando o método staircase. Experimentos adicionais como teste de tração e fadiga em corpos de prova fornecem dados suplementares sobre o material do virabrequim. Por fim, apre-sentamos um modelo de campo de fases para dano, fratura e fadiga para simular nucleação e propagação de trinca. Comentamos as discretizações espaciais e temporais para casos 1D e 2D, apresentando os resultados numéricos.
Palavras-chaves: Virabrequins; Metais - Fadiga; Automóveis - Testes; Métodos numéricos; Modelos de campo de fase.
Crankshafts are subjected to high loads in internal combustion engines, leading to bending and torsion stress cycles. Fatigue failure is a major concern when designing crankshafts, requiring several hours of fatigue testing, and the project becomes expensive and time consuming. With the objective of reducing test cost and time, we use finite element models to estimate test condi-tions and stress distribution of crankshafts under bending. We verify the accuracy of our model by comparing the numerical results with experimental data obtained from a resonant bending test rig that we designed and manufactured. The resonant test rig is used to obtain fatigue data of crank throw samples using the staircase method. Other experimental procedures such as spec-imen tensile and fatigue tests provide additional information on the crankshaft material. Last, we show a phase field model for damage, fracture and fatigue to simulate crack initiation and propagation. We comment on the spatial and time discretization of 1D and 2D approximations and show numerical results.
Keywords: Crankshafts; Metals - Fatigue; Cars - Testing; Numerical methods; Phase field mod-els.
Figure 1.1 – Schematic drawing of a four-cylinder crankshaft. . . 13
Figure 1.2 – Setup with the main equipments for the resonant fatigue test. . . 14
Figure 2.1 – Typical format of an S-N curve adapted from (NORTON, 2006). . . 18
Figure 2.2 – Sinusoidal waveform of rotating machinery loads. . . 19
Figure 2.3 – Mean stress effects to S-N curve (NORTON, 2006). . . 20
Figure 3.1 – Location of the specimens on the crankwebs. . . 28
Figure 3.2 – Tensile test specimen dimensions. . . 28
Figure 3.3 – Tensile test machine with specimen and strain gage. . . 29
Figure 3.4 – Monotonic tensile test specimen (a) Before the test; (b) After the test; (c) After the test with zoom in the fracture surface. . . 30
Figure 3.5 – Stress-strain curves for the monotonic tensile test of the six specimens. . . . 31
Figure 3.6 – Fatigue tensile test specimen (a) Before the test; (b) After the test. . . 33
Figure 3.7 – Screen shot of the controller’s oscilloscope for the first specimen showing load and displacement of the actuator. . . 34
Figure 3.8 – S-N curves for the experimental set, corresponding fully reversed axial and bending load cases. . . 35
Figure 3.9 – Samples after proper preparation for the SEM, cut from monotonic (left) and fatigue (right) specimens. . . 36
Figure 3.10–Scanning Electron Microscope and energy-dispersive X-ray spectroscopy equipments. . . 36
Figure 3.11–Monotonic tensile specimen fracture surfaces from the SEM. . . 37
Figure 3.12–Fatigue tensile specimen fracture surfaces from the SEM. . . 38
Figure 3.13–A typical output graph from X-ray analysis showing the proportion of chem-ical elements found (bottom left region of monotonic sample). . . 38
Figure 3.14–Indication of graphite sphere analyzed (circle). . . 39
Figure 3.15–Output graph from X-ray analysis of a specific point in a graphite sphere. . . 40
Figure 4.1 – Bending resonant test rig components. . . 43
Figure 4.2 – Assembly of the crank throw and internal sleeve showing the gap used to open the sleeve. . . 45
Figure 4.3 – Assembly steps of sleeve into inertia plates. . . 46
Figure 4.4 – Assembly steps of crank throw into internal sleeves. . . 47
Figure 4.5 – Final assembly of test rig. . . 48
Figure 5.1 – Boundary conditions for the static analysis: fixed support and remote force. . 50
Figure 5.2 – Comparison between crank throw original geometry and after the use of virtual topology. . . 51
topology. . . 51
Figure 5.4 – Comparison of coarse and fine meshes on the fillet surface. . . 51
Figure 5.5 – Convergence of the maximum principal stress in the fillet for different meshes. 52 Figure 5.6 – Maximum principal stresses in the crank throw. . . 53
Figure 5.7 – Maximum principal stresses in the crank throw with a cross-section cut in the centerline. . . 54
Figure 5.8 – Maximum principal stresses in the centerline of the bottom surface of the crankpin. . . 54
Figure 5.9 – Stress profile for the centerline of the bottom surface of the crankpin. . . 55
Figure 5.10–Finite element static moment and stress curve. . . 56
Figure 5.11–Comparison of sides of moment application. . . 56
Figure 5.12–Test rig modes of vibration and respective natural frequencies. . . 58
Figure 5.13–Natural frequencies for the first bending mode. . . 59
Figure 6.1 – Calibration relations and process. . . 62
Figure 6.2 – Strain gage length and respective positions on the crankpin surface. . . 63
Figure 6.3 – Strain gage locations in the crank throw sample. . . 63
Figure 6.4 – Setup scheme for the static calibration. . . 64
Figure 6.5 – Setup of experimental static calibration. . . 65
Figure 6.6 – Load measuring on HBM Scout 55. . . 65
Figure 6.7 – Static calibration charts for the crankpin journal strain gage. . . 66
Figure 6.8 – Static calibration charts for the crankpin Fillet 1 strain gage. . . 67
Figure 6.9 – Static calibration charts for the crankpin Fillet 2 strain gage. . . 67
Figure 6.10–Stress concentration factors of static calibration. . . 68
Figure 6.11–Correlation between experimental and finite element results of the stress at the crankpin center for different bending moments. . . 68
Figure 6.12–Inertia bars fixation scheme: steel wire passing through lifting eyes. . . 70
Figure 6.13–Inertia bars fixation with steel wires passing through lifting eyes. Note the holes used in the former fixation solution. . . 70
Figure 6.14–Stinger attachment to the shaker (left) and to the inertia plate (right). . . 71
Figure 6.15–Equipments used for the system excitation. . . 72
Figure 6.16–Accelerometer and signal conditioner used to obtain acceleration data. . . . 73
Figure 6.17–Complete dynamic test setup scheme and photographs. . . 74
Figure 6.18–Oscilloscope screen during resonance. Input (yellow) and acceleration re-sponse (blue) signals with phase difference of 106◦. . . 75
Figure 6.19–Dynamic calibration charts for the crankpin journal strain gage. . . 76
Figure 6.20–Dynamic calibration charts for the crankpin Fillet 1 strain gage. . . 76
Figure 6.21–Dynamic calibration charts for the crankpin Fillet 2 strain gage. . . 77
Figure 7.2 – Change of resonance frequency of first sample with number of cycles. . . . 86
Figure 7.3 – Possible crack locations in a crank throw under bending. . . 87
Figure 7.4 – Crack on the surface of the first sample: pink line on Fillet 1. . . 87
Figure 7.5 – Visual representation of staircase data. . . 88
Figure 7.6 – Change of resonance frequency for the fractured samples of the staircase method. . . 88
Figure 7.7 – Rate of change of resonance frequency for the fractured samples of the stair-case method. . . 89
Figure 7.8 – Samples cut from the first and second crank throw samples. The arrows in-dicate the crack location in the crankpin fillet. . . 90
Figure 7.9 – Crack location and path of sample 1. . . 91
Figure 7.10–Crack length measurement of sample 1. . . 91
Figure 7.11–Crack location and length measurement of sample 2. . . 92
Figure 7.12–Zoom in the crack path of sample 2 with different amplification magnitudes. 92 Figure 8.1 – Time evolution of damage and fatigue under monotonic and sinusoidal load for 1D bar (BOLDRINI et al., 2016). . . 98
Figure 8.2 – S-N curve (BOLDRINI et al., 2016). . . 98
Figure 8.3 – Relative errors and computational time for different time increments (MORAES et al., 2017). . . 100
Figure 8.4 – Damage evolution in the test specimen for a sinusoidal loading (MORAES et al., 2017). . . 100
Figure 8.5 – Time evolution of damage and fatigue under monotonic and sinusoidal load for 2D I-shaped specimen (MORAES et al., 2017). . . 101
Figure 8.6 – Nothced tensile test (CHIARELLI et al., 2017). . . 101
Figure 8.7 – Notched tensile test crack patterns for different values of γ (CHIARELLI et al., 2017). . . 102
Figure A.1 – Inertia plate drawing with dimensions in mm. . . 110
Figure A.2 – External sleeve drawing with dimensions in mm. . . 111
Table 3.1 – Measured dimensions of the monotonic tensile test specimens. . . 28
Table 3.2 – Monotonic tensile test strain gage results for the six specimens. . . 29
Table 3.3 – Monotonic tensile test load results for the six specimens. . . 29
Table 3.4 – Fatigue tensile test life results for the six specimens . . . 33
Table 3.5 – Corresponding fully reversed fatigue strength of specimens using the modified-Goodman relation. All stresses are given in [MPa]. . . 34
Table 3.6 – Element proportions in mass percent for the bottom left region of the mono-tonic sample and the average of all regions. . . 39
Table 3.7 – Element proportions in mass percent of a specific point in a graphite sphere. . 39
Table 5.1 – Static analysis mesh convergence for different element sizes. . . 52
Table 5.2 – Stress ratios between pin fillet and pin center. . . 55
Table 5.3 – Material properties for structural steel and cast iron. . . 57
Table 5.4 – Modal analysis results of natural frequencies. . . 58
Table 5.5 – Modal analysis mesh convergence for different element sizes. . . 59
Table 7.1 – Load levels for the first crank throw sample. . . 85
Table 7.2 – Staircase fatigue data . . . 89
1 Introduction . . . 13
1.1 Objectives . . . 16
1.2 Dissertation organization . . . 17
2 Literature review . . . 18
2.1 Fatigue failure . . . 18
2.2 Crankshaft fatigue assessment . . . 21
2.2.1 Crankshaft design, materials and manufacturing . . . 22
2.2.2 Numerical and experimental crankshaft fatigue assessment . . . 23
3 Material characterization . . . 26
3.1 Monotonic tensile tests . . . 26
3.2 Specimen tensile fatigue tests . . . 32
3.3 Scanning Electron Microscope (SEM) Analysis . . . 35
3.3.1 Fracture surface analysis . . . 36
3.3.2 Chemical composition analysis . . . 37
3.4 Conclusions . . . 40
4 Resonant bending fatigue test rig . . . 42
4.1 Test rig design . . . 43
4.1.1 Inertia plates . . . 43
4.1.2 External sleeves . . . 44
4.1.3 Internal sleeves . . . 44
4.1.4 Comments on materials and manufacturing . . . 45
4.2 Test rig assembly . . . 45
4.3 Conclusions . . . 48
5 Finite element analysis . . . 49
5.1 Static analysis . . . 49
5.1.1 Convergence analysis . . . 49
5.1.2 Stress analysis . . . 52
5.1.3 Comments about the side of moment application . . . 55
5.2 Modal analysis . . . 57
5.3 Conclusions . . . 60
6 Test calibration . . . 61
6.1 Calibration fundamentals . . . 61
6.2 Static calibration . . . 62
6.2.1 Strain gage positioning . . . 62
6.2.2 Static calibration setup . . . 64
6.3.1 Test setup . . . 69
6.3.1.1 Test rig fixation . . . 69
6.3.1.2 Comments on stinger fixation and positioning . . . 70
6.3.1.3 Data acquisition and final setup . . . 71
6.3.2 Resonance frequency identification . . . 72
6.3.3 Dynamic calibration results . . . 75
6.4 Conclusions . . . 78
7 Crankshaft fatigue test . . . 79
7.1 Fatigue test procedure . . . 79
7.2 Statistical considerations of crankshaft fatigue analysis . . . 80
7.2.1 Fatigue strength estimate . . . 81
7.2.2 Step size . . . 81
7.2.3 Number of samples . . . 82
7.2.4 Data reduction models . . . 83
7.3 Determination of the fatigue strength range . . . 84
7.4 Staircase results . . . 87
7.5 Crack analysis . . . 90
7.6 Conclusions . . . 92
8 A phase field approach to material damage and fatigue . . . 94
8.1 Governing equations . . . 95
8.2 1D simulations . . . 97
8.3 2D simulations . . . 99
8.4 Conclusions . . . 102
9 Conclusions . . . 103
9.1 Suggestions for future works . . . 104
References . . . 106
APPENDIX A Test rig components drawings . . . 110
1 INTRODUCTION
Crankshafts are one of the main components of internal combustion engines, as they transform the reciprocating motion of the pistons into rotational motion. They are sub-jected to the highest loads in the engine cranktrain, leading to bending and torsion stress cycles. These alternating stress cycles could lead to fatigue failure, which is the most common failure mechanism in engineering components.
Figure 1.1 shows a typical four-cylinder crankshaft and its main components. The main bearing journals are supported by the engine block. The crankpins, off-centered from the main bearing journal are attached to the connecting rods. A crank throw consists of two full main bearing journals and one crankpin, as illustrated in Figure 1.1. Fillets of crankpins and journals are the most critical locations of a crankshaft, due to high stress concentrations caused by high stress gradients on these locations (CHIEN et al., 2005).
crankthrow main journal crankpin crankwebs fillets crankfront crankend
Figure 1.1 – Schematic drawing of a four-cylinder crankshaft.
The stress concentration on the fillets may lead to a fatigue crack nucleation on these regions. Several techniques are used to enhance fatigue life on the critical zones, such as shot-peening, deep rolling, nitriding or induction hardening, which all induce compressive residual stresses, raising the fatigue life of the crankshaft even under high stresses on the fillets. The critical condition on the fillet regions requires a robust and reliable fatigue life assessment of the crankshafts. Over the years, many techniques were developed to perform bending fatigue tests of crank throws, the most common in industry being resonant fatigue tests (YU et al., 2004; CHIEN et al., 2005; SPITERI et al., 2005; VILLALVA; JUNIOR, 2010). They operate by tracking the resonance frequency of the testing system using a "tuning fork" structure, attaching two heavy plates to the crank throw, as illustrated in Figure 1.2 . The use
of a resonant system allows for faster test times and smaller input loads, and allows for crack detection in an automated way, using an accelerometer to track frequency shifts. Cracks in the structure decrease the component’s stiffness, thus decreasing the resonance frequency (GUD-MUNDSON, 1982). The decrease of the resonant frequency after a certain limit is considered a component failure and the test is suspended.
Accelerometer Shaker Data acquisition system Inertia plates Crank throw
Figure 1.2 – Setup with the main equipments for the resonant fatigue test.
The fatigue or endurance limit is a stress below which the material can endure infi-nite life cycles. In polished controlled specimens, it appears as a knee in the S-N diagram, but for real component fatigue tests, the definition of a fatigue limit is arbitrary. Typically when testing crankshafts, the fatigue limit is usually obtained for 2, 5 or 10 million cycles. Due to variability of material, surface or even test conditions, fatigue data has a statistical nature (LEE, 2005). The statistical properties of crankshaft fatigue, such as mean fatigue limit and standard deviation, can be calculated by different methods, the most common being the up-and-down or staircase method (DIXON; MOOD, 1948). The requirement of testing several samples raises significantly the cost and time for fatigue testing of crankshafts, and ask for different approaches to reduce such expenses.
The use of numerical models and simulation reduce the number of prototypes, which leads to cheaper development. Furthermore, computational modeling makes the develop-ment of components evolve in faster rates by reducing the need to manufacture prototypes and perform testing at each iteration step of the project. However, to rely on results obtained from a computational model, it is necessary to correlate the numerical solution with data obtained
from experimental testing. We can adjust parameters and settings of the simulations to calibrate the virtual model. Some parameters like mesh refinement, appropriate constitutive relations and boundary conditions are some of the most common adjustments.
The finite element method is a powerful tool to provide information about stress distribution in the crankshaft and stress concentration on the crankpin and main journal fillets. Finite element modal analysis provide information about the resonant frequencies of the test rig, which can be used in a harmonic analysis to study the response of the crankshaft and test rig when in resonance. Fatigue life can be estimated using finite element analysis and then compared to experimental results to validate the model.
A recent trend in automotive industry is the manufacturing of compact lightweight engines and components. The challenges of this new design pattern is to assure the same per-formance whilst operating with smaller and lighter components. In the case of crankshafts, a weight reduction should care for the stress concentration not only in the fillet regions but also in many other areas, since the change in geometry will alter the stress distribution. Also, new fatigue tests would be necessary to validate the new lightweight geometries. Again, numeri-cal analysis plays an important role in the evaluation of new crankshaft designs with reduced weight.
However, standard numerical methods still lack the ability to predict crack initiation and propagation. Either we only verify the stress concentration and identify a possible crack lo-cation, or we already know the crack location and length a priori and then solve for the crack propagation. Phase field models can predict crack initiation and propagation and have been used to simulate brittle and ductile fracture (MIEHE et al., 2010; AMBATI et al., 2015). Ini-tially used to model fluid separation (CAHN; HILLIARD, 1958), phase field models have been used to solve complex interface problems. For fracture models, cracks are modeled as smooth diffuse interfaces, which successfully capture different phenomena as initiation, branching and coalescence, representing large advantage over sharp interface models. Another advantage of phase field models is the possibility to derive thermodynamically consistent models, even for complex situations involving fracture and fatigue.
More recently, fatigue behavior was also modeled using phase fields in a thermody-namically consistent way (BOLDRINI et al., 2016). This novel technique couples damage and fatigue effects in a general way, where the use of different free-energy potentials can change material behavior, damage reversibility, include temperature effects and plasticity, among other modifications. If properly validated and calibrated, phase field models for fracture and fatigue can significantly help in the design of mechanical components, such as crankshafts, by indi-cating possible fracture locations, damage distribution and estimating fatigue life for complex systems.
In this work, we will show a review of the phase field framework in (BOLDRINI et al., 2016) and fracture and fatigue results for 2D specimens under monotonic and cyclic tensile
loading from (CHIARELLI et al., 2017) and (MORAES et al., 2017). The 2D models shall be used in the future to simulate the experimental results of specimens cut from the crankshaft samples to study the influence and sensitivity of the phase field model parameters, allowing a precise correlation between tensile and fatigue numerical simulations with their respective experiments. This simpler correlation using specimens is a first step to use phase field models in more complex geometry and test conditions, such as a 3D crankshaft.
1.1 Objectives
This work has three different approaches, that combined can provide important in-formation about the fatigue characteristics of crankshafts, leading to a more accurate evaluation of the fatigue strength. The different aspects of this work are: experimental fatigue assessment of crankshafts, numerical analysis of crankshafts, and the application of a phase field model for structural fracture and fatigue.
The first objective is to design and build an experimental resonant test rig for bend-ing fatigue testbend-ing of crankshafts. Based on the work of many researchers, along with industry standards and guidelines, we will develop and validate several test procedures including: assem-bly and positioning of the test rig, instrumentation, sensor calibration, test control and statistical analysis. We will run fatigue tests of cast iron crank throw samples of light vehicles supplied by PSA Group from Brazil. Additional experiments are helpful to correctly identify material characteristics and properties for fatigue strength estimation and for numerical analysis input, such as specimen tensile and fatigue tests and chemical composition. At the end of this work, we will have obtained the necessary skills and experience to adapt the test for new designs of lightweight crankshafts, and to develop torsion fatigue tests in the future.
Numerical analysis of crankshafts is the second objective of this work. We will use commercial software for the finite element analyses of the bending test rig and crankshaft geometry. For the bending test rig, modal analysis of the complete assembly gives the resonance frequencies and their respective modes of vibration. This is helpful to identify the resonant frequency in the fatigue test, assuring that we will dwell in the bending mode of vibration. Static analysis of the crank throw provides the stress distribution when applying moment conditions equivalent to experimental loadings. This allows to verify the stress concentration on the fillets and to identify the effects of fillet rolling by comparing the numerical and experimental results of stress concentration.
While the existing finite element analysis softwares solve classic problems in a ro-bust way, we want to be able to study crack initiation and propagation under fatigue effects. In order to see this phenomena in a crankshaft, we need first to develop such model in a consis-tent way. Therefore, the third objective is to apply a phase field framework to model damage evolution, fracture and fatigue. We will present the many features of the model. We will discuss the numerical methods and comment the results of three main papers derived from the model.
The first paper shows the complete derivation of the equations and important results for 1D high-order finite element approximation, temperature effects and a qualitative S-N curve with fatigue effects (BOLDRINI et al., 2016). The other papers show 2D implementations of the phase field model. In (CHIARELLI et al., 2017), the main focus is in spatial convergence and effects of the phase field layer width, with benchmark test results for crack propagation. The last work, (MORAES et al., 2017) shows the convergence study of different time integration schemes. All these works shall contribute to simulate tensile and fatigue test in specimens sim-ilar to the ones considered in this work. From these 2D tests, many phenomenological aspects can be simulated, such as crack initiation and propagation, the influence of fatigue in cyclic loading and S-N curves. The calibration and validation of 2D models will be helpful to test 3D crank throw geometry and identify crack initiation of new weight reduced designs in the future, which may present stress concentration on different locations when compared to the original crankshaft geometry.
1.2 Dissertation organization
This dissertation is organized as follows. Chapter 2 will present the literature review of the main principles and definitions of mechanical fatigue and crankshaft fatigue assessment. Chapter 3 will show results of the material characterization of the crankshaft samples used in this work, including specimen tensile and fatigue tests and chemical composition. The design and assembly procedure of the bending resonant test rig will be presented in Chapter 4. Chap-ter 5 will show the methodology and results of static and dynamic finite element analyses of the crank throw and test rig. In Chapter 6, we will discuss the static and dynamic calibration procedures, used to establish a relation between the desired bending moment and acceleration, which is used as the tracking parameter for failure. Chapter 7 will show the procedure and re-sults for crank throw fatigue tests. The phase field model will be presented in Chapter 8 along with comments on the main results derived from the papers published. Finally, Chapter 9 will address the main conclusions of this work and discuss suggestions for future works.
2 LITERATURE REVIEW
This chapter aims presents the literature review on the most relevant topics of this work. We will discuss basic concepts of fatigue failure and a review of the state-of-the-art techniques and results of crankshaft fatigue testing.
2.1 Fatigue failure
Time varying loads are the most common cause of failure in engineering, occurring at stress levels typically lower than the material yield strengths. This phenomenon started to appear in the 19th century when railroad-car axles broke in a brittle-like manner even with the use of ductile steels (NORTON, 2006).
The systematic study of fatigue failure in materials began with August Wohler in 1855. In his study, Wohler showed that fatigue occurs by the growth of a crack that initiated at the component’s surface. He investigated axle failure under fully reversed loadings and built a curve that related the stress of a component to the number of cycles it can endure. This relation is called a S-N curve, or Wohler curve.
Wohler also showed that some materials, such as steels can endure millions of life cycles if loaded below a given stress limit, called endurance limit. Figure 2.1, adapted from (NORTON, 2006), shows a typical S-N curve for materials with and without an endurance limit. Typically non-ferrous materials do not possess an endurance limit.
σf
σf
σut
Figure 2.1 – Typical format of an S-N curve adapted from (NORTON, 2006).
The endurance limit is also called fatigue limit, and is denoted by σf. The fatigue
life Nf of a component is defined as the number of cycles of stress or strain it sustains before
failure. The stress value for a fatigue life of Nf cycles obtained from the S-N curve is called the
Fatigue failure presents three stages. The first stage is the crack initiation, where localized plastic yielding may coalesce and form a microscopic crack. The second stage, the crack propagation, may take the most part of the component’s life. In this stage, the cracks grow slowly at each cycle due to tensile stresses at the crack tip. The crack grows until the stress intensity factor K at the crack tip surpasses the materials fracture toughness Kc, causing
sudden and catastrophic failure (NORTON, 2006).
Different types of time-varying loads may cause different effects on fatigue failure. Figure 2.2 shows a typical sinusoidal waveform used to represent the time load from rotating machinery, such as crankshafts. In order to identify the parameters that change the character-istics of the waveform, we need to use some relations in terms of the maximum and minimum stress values of the sine wave, σmaxand σmin, respectively.
Str
ess
Time
+
-Cycle (2 reversals) a min max m ΔσFigure 2.2 – Sinusoidal waveform of rotating machinery loads. The stress range is defined by:
∆σ = σmax− σmin. (2.1)
The alternating stress is the amplitude of the sine wave and computed from:
σa=
σmax− σmin
2 . (2.2)
The mean stress is
σm=
σmax+ σmin
2 . (2.3)
Additionally, we define the stress ratio as
R= σmin σmax
and the amplitude ratio as
A= σa σm
. (2.5)
A fully reversed loading is characterized by a zero mean stress, resulting in a stress ratio R = −1 and amplitude ratio A = ∞. In the case of a fully tensile load, the mean stress is grater than zero, and the stress ratio is R > 0. It is important to know what type of load the component is subjected. For example, in the case of the resonant bending test rig presented in Chapter 4, the stress ratio is R = −1 due to the bending mode of vibration. In the case of specimen fatigue tests developed in Chapter 3, the stress ratio is R = 0.1. In order to correlate the fatigue strength of specimen and crankshaft, we need to take into consideration the effects of the mean stress.
A positive mean stress adds a tensile component to the alternating stress value, making the material fail at a lower stress when compared to a fully reversed load, as illustrated in Figure 2.3. Conversely, a compressive mean stress is beneficial to the specimen, making it fail at higher stresses. That is why crankshaft manufacturers often employ surface treatments that induce compressive residual stresses to the fillet surfaces.
Figure 2.3 – Mean stress effects to S-N curve (NORTON, 2006).
In order to take into account the mean stress effects, we use the modified-Goodman line which connects the fatigue strength in the alternating stress axis to the ultimate stress in the mean stress axis. This is a more conservative approach and commonly used failure criterion to design components with positive mean stress (NORTON, 2006). The modified-Goodman
failure line is defined by: σa= σf 1 −σm σut , (2.6)
where σf is the fatigue strength for a zero mean stress load and σut is the ultimate stress. We
use Equation (2.6) to compute the equivalent fully reversed fatigue strength σf from data with
a nonzero mean stress.
In the specimen fatigue tests of Chapter 3, we obtain data for an axial load, while the crankshaft will be subjected to bending load in the resonant test rig. Thus, we also need to correct the effect of axial load in order to compare the fatigue strength for both cases. Axial test results may be 10 − 30% lower than bending fatigue tests for the same specimens (NORTON, 2006). Therefore, the results of our specimen fatigue tests must be corrected by that amount to correspond to the bending fatigue strength.
2.2 Crankshaft fatigue assessment
Crankshafts are the most loaded components of internal combustion engines and not allowed to fail under service. These facts led to years of research involving different aspects of crankshaft design. Some of the topics studied involve crankshaft materials and manufactur-ing, surface treatments, dynamic analysis, fatigue assessment and life estimation. Moreover, researchers extensively studied practical aspects of fatigue tests, such as failure criterion, test control and statistical aspects.
Among all studies, we highlight three articles that summarize most of the aspects of crankshaft design, manufacturing and testing. The first one is a study on fatigue performance of forged steel and cast iron crankshafts (WILLIAMS et al., 2007), in which authors discuss broad aspects of fatigue life, using information from tensile, fatigue and impact tests of specimens, be-sides component fatigue tests. They also studied stress concentration using finite element analy-sis (FEA) to predict fatigue life. The second part of this work (MONTAZERSADGH; FATEMI, 2007b) focused on the weight and cost optimization of forged steel crankshafts. Dynamic and stress analysis using FEA were compared to experimental results. The third reference work is a literature review on different aspects of crankshaft fatigue evaluation (ZOROUFI; FATEMI, 2005).
All three works mentioned are a combination of multiple articles written over the years and discuss a broad range of topics. The contents of the three reference works and the articles that originated them will now be discussed in detail.
2.2.1 Crankshaft design, materials and manufacturing
Crankshafts for automotive applications are most commonly made of steel or ductile iron. The choice between each material takes into account different aspects other than perfor-mance, such as material cost, weight and manufacturing process. Steel crankshafts are used in forging while iron crankshafts are cast. After the casting or forging, crankshafts may go un-der heat or surface treatment in orun-der to enhance its fatigue strength. The use of microalloyed steels can reduce manufacturing costs by eliminating the need of heat treatments (ZOROUFI; FATEMI, 2005).
While it was observed that cast iron crankshafts cost less for high volume pro-ductions (ZOROUFI; FATEMI, 2005), forged steel crankshafts show higher fatigue strength as studied in the works of (WILLIAMS; FATEMI, 2007; WILLIAMS et al., 2007). In (WILLIAMS; FATEMI, 2007), researchers compared the fatigue performance of forged steel and cast iron crankshafts using several different tools. They cut specimens from the crankshafts to obtain material properties from tensile, fatigue, impact and hardness tests. They showed that fatigue has a softening effect on forged steel and a hardening effect on cast iron under cyclic loads. Forged steel crankshafts also showed longer fatigue life when compared to cast iron.
Also in the work (WILLIAMS; FATEMI, 2007), they compared experimental strain gauge measures with results obtained with FEA for a crankthrow under bending and obtained good correlation. Stress life estimates for the forged steel crankshaft were more accurate than for cast iron, while cast iron estimates were more conservative.
Strain-life of cast iron crankshafts were studied in (TARTAGLIA, 2012). Author studied monotonic tensile, hardness and fatigue tests of ductile irons with different chem-ical compositions and under different heat treatments and built a robust mechanchem-ical prop-erty database. Heat treatment is an important process that increases the fatigue strength of crankshafts, the most common being the induction hardening. Hardening effects were stud-ied in (GRUM, 2003). Author showed residual stress distributions due to hardening, illustrating the compressive nature of residual stresses as well as the depth of the surface affected by the heat treatment. The work also discuss the effects of grinding on the treated surface.
Another common surface treatment for crankshafts is nitriding, which was studied in (PARK et al., 2001). Authors compared the effects of nitriding and fillet rolling on fatigue strength and observed that 900 kg f fillet rolling force and nitrided samples had 80% increase in fatigue strength. Due to its relatively low costs and good fatigue strength improvement, fil-let rolling is largely used in industry. Many researchers studied the effects of deep rolling in crankshafts using both experimental and numerical methods.
The influence of deep rolling on a cast iron crankshaft was studied in (CHIEN et al., 2005). In this paper, authors review the process of bending resonant fatigue tests. The stress concentration near the fillets was investigated using an elastic finite element model. An
elasto-plastic model was later used to study the effects of the deep rolling on the stress distributions near the fillets. Bending simulations of unrolled crankthrows were compared to rolled ones, which showed less stress concentration on the fillets due to residual stresses. Additionally, they used linear elastic fracture mechanics to analyze the fatigue crack propagation by defining an effective stress intensity factor combining the bending moment and residual stress effect.
The four-bubble appearance is a criterion used by (LEE; MORRISSEY, 2001) and others to determine failure through the initiation of micro-cracks on the fillet surfaces, defined by the appearance of four bubbles in a quarter inch. As well as (CHIEN et al., 2005) would observe and study years later, Lee and Morrissey concluded that the four-bubble criterion, be-sides being too conservative, did not correlate well with the fracture of crankshaft subjected to deep rolling, as it does not indicate whether cracks would propagate or arrest in the compressive zone.
The effects of fillet rolling were investigated analytically and experimentally in (SPITERI et al., 2007). The work compared different failure criteria, namely, crack initiation, resonant shifts and two-piece failure, which is the complete fracture of the crank throw in two separate parts. They concluded that crack initiation was a conservative criterion as it does not take the crack arrest into account, reducing the fatigue limit of the crankshaft. They also used finite element simulations of the deep rolling process to evaluate the residual stresses near the fillets.
One of the most impressive results of the effects of fillet rolling was obtained by (KAMIMURA, 1985). In this paper, he derived a direct relation between the rolling force and ductile cast iron crankshaft bending stress. Compared to bare samples, rolled fillets have a fa-tigue strength more than two times higher, going from 191 MPa without rolling up to 412 MPa. In his master’s dissertation, (FONSECA, 2015) performed an in depth review on deep rolling and developed a methodology to run plastic transient finite element analysis in order to estimate the effects of fillet rolling.
2.2.2 Numerical and experimental crankshaft fatigue assessment
One of the first works on experimental fatigue strength of crankshafts was (JENSEN, 1970). Author tested V8 crank throws in a resonant bending test rig and obtained stress data from critical locations of the crankshaft under operation conditions. Jensen developed calibra-tion procedures for different load condicalibra-tions using strain gages for bending and torsion and obtained an S-N curve for the crankshafts.
Years later, another reference work for crankshaft fatigue assessment was developed (LEE; MORRISSEY, 2001). They also obtained operating loads experimentally similarly to (JENSEN, 1970). Additionally, they also tested crankshaft fatigue strength using resonant bend-ing tests, but looked into other aspects of the procedures. They used a ray-projection method
to estimate fatigue life and compared the fatigue limit for different surface hardness using the four-bubble criterion, which did not result in improvements on the fatigue limit. One important conclusion of their work is the definition of a number of cycles to determine the fatigue limit, when it does not exist, from 2 × 106to 107cycles.
Since the four-bubble criterion was conservative and did not correlate well with the failure of crankshafts, a different criterion was necessary to detect cracks with more precision. The principle used for the failure criterion is that in the presence of cracks, notches or other geometry changes, the resonance frequency of the body changes (GUDMUNDSON, 1982). Gudmundson showed that effect mathematically, and presented finite element results of beams with different cracks. Based on this principle, (FENG; LI, 2003) developed computerized and automated test routines that can both detect a frequency shift and control the test. They devel-oped a controlling system with two closed loops: one that controls the load and keeps it constant during test, and another one that tracks the frequency shift and excites the system at the new resonance frequency.
Also in (FENG; LI, 2003), they elaborated on the load calibration principles for the fatigue resonant test. They showed that the bending moment applied to the specimen is difficult to measure directly and can be determined only by acceleration. They introduced the strain as an intermediate quantity and suggested static and dynamic calibrations. The static calibration measures the strain and the moment accurately. The dynamic calibration uses the strain and acceleration in such way that we have a relation between these three variables.
Another work on controlling the resonant test was proposed by (PATEL; SPITERI, 2006). They developed an automate system that can run fatigue tests until failure or suspension. This system can also track possible resonance frequency shifts and adjust the load to a pre-established desired load. They observed that frequency sweeps account for most lost time in the test, and studied a tolerance to make the frequency sweeps more or less frequent.
The failure criterion based on resonant frequency drops was further studied in (YU et al., 2004). They quantified the change in the resonant frequency as a function of crack depth. Natural frequencies of resonant systems with crankshaft sections for notches varying from 1 to 5 mm were obtained experimentally and then compared to finite element models, which showed good correlation.
Frequency drop criterion was applied to study failure modes of cast-iron crankshafts in (SPITERI et al., 2005). They monitored the resonance shifts, stiffness changes and cracks, observing that the resonance shift criterion is sufficient to indicate two-piece failure. A staircase method was employed to obtain the mean fatigue strength of V6 and V8 crankshafts. Surface cracking was apparent early on, even with no change in resonance until an abrupt and acceler-ating resonant shift showed cracks with depth from 8 to 15 mm. The changes in frequency were negligible for the most of the test, and a 2 Hz or 3% frequency shift would capture 90% of the to-tal cycles. Another important observation is that significant changes in the resonance frequency
did not occur in suspended tests where the crank throw survived. Another important aspect of the work is the comparison between the resonant shift criterion and crack surface criterion when assessing the mean fatigue strength. A surface failure method, such as the four-bubble, under-estimated the two-piece failure fatigue strength, since the four-bubble cracks appeared during every test, in agreement with (LEE; MORRISSEY, 2001) and (CHIEN et al., 2005). Conse-quently, they concluded that the resonant shift is a valid failure criterion that correlates well with two-piece failure.
In the work (MONTAZERSADGH; FATEMI, 2007a), researchers conducted finite element dynamic simulations of crankshafts. The pressure curve of an engine cylinder was employed to compute the loads acting on the crankshaft for different engine rotations. Those loads were then used to calculate the stresses in the crankshaft, thus obtaining a critical rotation and region. They correlated these results to experimental tests. One important aspect of this work is the use of a dynamic simulation instead of static assessment, which overestimates the stress levels in the crankshaft. They claim that torsion effects due to the dynamic loadings only can be neglected as they are very low when compared to bending stresses.
Dynamic simulations were also used in (MONTAZERSADGH; FATEMI, 2008). They used the results of the dynamic analysis in the optimization of the geometry, material and manufacturing process of the crankshaft aiming to improve the fatigue strength. The main criterion for the optimization was to guarantee that stresses in the optimized geometry would not exceed the stresses in the critical locations. In order to respect the interchangeability with the original crankshaft, only some features could be optimized, such as thickness and geometry of the crank web, inner hole dimensions and the outer section of the crankpin bearing. Those locations support weight reduction because they present low stresses under operation loading.
Besides geometry optimization, authors also considered changes in the manufactur-ing process with the inclusion of fillet rollmanufactur-ing. Moreover, they also evaluated the use of microal-loyed steel to eliminate the heat treatment, reducing manufacturing costs. At the end, authors reduced the weight of the crankshaft in 18% without changing dimensions of the engine block or the connecting rod, while preserving the balance of the crankshaft.
Fatigue strength resulted from resonance tests were correlated to finite element models in (VILLALVA; JUNIOR, 2010). In this work, authors simulated both bending and torsional tests. They used a crank throw subjected to a remote force in the static analysis and the results of stress distributions have a good correlation to strain gauge measurements from the bench of fatigue tests. The deviation, computed between computational and experimental models, is less than 1% for stress at the fillet radius in the bending test. For the torsional tests, a deviation of 4.52% was obtained on the bottom center of the crank pin for a non-symmetric crank throw. For a symmetric crank throw in torsion, the deviation was 1.17%. This procedure will allow us to calibrate the finite element model of our crankshaft using experimental data in a straightforward way.
3 MATERIAL CHARACTERIZATION
In order to understand the fatigue behavior of crankshafts, we need different tech-niques and fields of knowledge. Ranging from numerical methods and programming to instru-mentation and modal testing, the objective of identifying the fatigue characteristics of crankshafts is complex and broad. Among all the subjects and details involved in crankshaft fatigue anal-ysis, whether it is experimental or numerical, we highlight one common element of both ap-proaches which affects directly the methods, the results and their interpretation. That element is the crankshaft material.
Studying the material characteristics, its microstructure and main properties allows to better evaluate the results of the component’s fatigue test, and even predict some of the results. Furthermore, we have the possibility to identify deficiencies and disadvantages of using the current material and apply different manufacturing processes, treatment, or even choose another material that will better meet the requirements for the crankshaft.
Crankshafts are usually made of forged steel or cast iron. Forged steel crankshafts may employ microalloyed steel in order to eliminate the heat treatment (WILLIAMS et al., 2007). Forged steels are more ductile and more resistant to impact than cast irons (WILLIAMS; FATEMI, 2007). For those reasons, they also show higher fatigue strength when compared to cast iron crankshafts, which makes forged steel better suited for heavy applications such as Diesel engines.
However, forged steel crankshafts are more expensive than nodular cast iron ones, which are a better choice for applications that require less strength, such as light vehicles (ZOROUFI; FATEMI, 2005). That is the case of most passenger cars and is the focus of this work. We begin the assessment of fatigue strength of cast iron crankshafts by its material char-acterization.
First, we will show the specimens, test conditions and results for the monotonic tensile tests, which include the main mechanical properties of the cast iron. Then, we show the specimen fatigue test procedures and results, where we obtain the S-N curve for a load ratio R= 0.1. We then observe the fracture surfaces in a Scanning Electron Microscope (SEM) in order to verify the failure characteristics. We also use an Energy Dispersive X-ray Spectroscopy (EDS) to identify the chemical composition of the material.
3.1 Monotonic tensile tests
Some of the most important mechanical properties of engineering materials are ob-tained directly from tensile tests. Properties like Young modulus E, yield stress σy, percent
re-sistance. Additionally, other properties can be estimated from tensile test data. The ultimate stress can be used to estimate fatigue strength, or to compute the modified-Goodman relation described in Chapter 2, where an equivalent fully reversed fatigue strength is obtained from mean and alternating stress components.
Many of the data obtained from tensile test can be used in finite element models, as most equations of solid mechanics were developed taking those properties in mind, such as the Young modulus E. The most simple example of the use of the Young modulus is the modeling of linear elastic materials.
Tensile test is an established procedure to understand material behavior with stan-dards from several different institutions. For the tests of this work, we used ASTM procedure (ASTM E8M - 15a, 2015). The ASTM standard presents guidelines for the specimen dimen-sions, positioning and gripping. Furthermore, the standard gives information regarding strain gage positioning, test speed and control, and mechanical properties determination.
We designed the tensile test specimen based on the ASTM standard, but also con-sidering some limitations of the test machine. The minimum length required for the specimen to insert the strain gage was 100 mm. Any specimen smaller than this would make the grips too close to each other, making it impossible to insert the strain gage. Limited by the speci-men length, and observing that the maximum dispeci-mension of a circular specispeci-men cut from the crankshaft bearing would be 54 mm, it was not possible to obtain circular specimens from the main journals.
The location of the crankshaft that would allow the machining of a 100 mm speci-men was the crankweb. Figure 3.1 illustrates the specispeci-men location on the crankwebs and Figure 3.2 shows the specimen dimensions. Although the crankwebs admit longer dimensions for the specimens, they are limited in shape, being necessarily flat. For the monotonic tensile test this fact has no impact in the manufacturing of the specimens, but poses difficulties and raises the cost of fatigue specimens, due to the process of grinding and polishing, much harder in flat specimens when compared to circular ones.
Six specimens were manufactured and tested in a 100 kN MTS 810-Flextest40 servo-hydraulic, at the LEM (Laboratório de Ensaios Mecânicos) of the School of Mechan-ical Engineering (FEM) at the State University of Campinas (UNICAMP). The test ran at as speed of 3 mm/min. The strain gage had a 25.4 mm length, and the data acquisition rate was 20 Hz. The measured width, thickness and area of the central cross-section of the specimens are shown in Table 3.1, along with the mean and standard deviation. This information are used to compute the stresses by the test software.
Figure 3.3 shows the MTS test machine with the specimen, the grips and the posi-tion of the strain gage. Figure 3.4 shows the specimen before and after the tensile test, as well as a zoom of the fracture surface.
Figure 3.1 – Location of the specimens on the crankwebs. 100.00 32.00 1 0 .0 0 6.00 6 .0 0 R6.00
Figure 3.2 – Tensile test specimen dimensions.
Table 3.1 – Measured dimensions of the monotonic tensile test specimens. Specimen # Thickness [mm] Width [mm] Area [mm2]
1 5.90 5.20 30.68 2 5.50 6.00 33.00 3 6.00 5.95 35.70 4 6.00 5.95 35.70 5 5.90 5.90 34.81 6 6.00 5.90 35.40 Mean 5.88 5.82 34.22 Std. Dev. 0.19 0.30 2.01
Grips
Specimen
Strain gage
Figure 3.3 – Tensile test machine with specimen and strain gage.
Table 3.2 summarizes the results of the monotonic tensile test for the six specimens using strain gage data. The measured and percent elongation are obtained from strain gage data at the end of the test. Table 3.3 shows the test results for load data. The yield stress is defined as the stress at an offset of 0.2 %. It is calculated as the load at the offset divided by the cross-section area of the specimen in Table 3.1. Similarly, the ultimate stress is calculated as the ratio between the maximum (or peak) load during the test by the cross-section area.
Table 3.2 – Monotonic tensile test strain gage results for the six specimens.
Specimen # Measured Elongation [mm] Percent Elongation [%] Young Modulus [GPa]
1 25.95 3.8 -2 25.95 3.8 197.86786 3 26.00 4.0 152.29388 4 26.05 4.2 183.15488 5 25.90 3.6 185.43553 6 25.90 3.6 169.61104 Mean 25.96 3.8 177.67264 Std. Dev. 0.06 0.2 17.37264
Table 3.3 – Monotonic tensile test load results for the six specimens. Specimen # Load at Offset
Yield [N]
Stress at Offset
Yield [MPa] Peak Load [N] Ultimate Stress [MPa]
1 13682.3954 445.9712 22033.5600 718.1734 2 14221.3865 430.9511 25294.5111 766.5003 3 13384.0487 374.9033 24520.5369 686.8498 4 14176.9350 397.1130 25413.9241 711.8746 5 12795.1012 367.5697 23525.6380 675.8300 6 13581.4370 383.6564 24405.8973 689.4321 Mean 13640.2173 400.0275 24199.0112 708.1100 Std. Dev. 531.2064 31.7122 1262.13507 32.7651
(a)
(b)
(c)
Figure 3.4 – Monotonic tensile test specimen (a) Before the test; (b) After the test; (c) After the test with zoom in the fracture surface.
Note that the result for the Young modulus of specimen 1 was discarded in Table 3.2. During the test, the strain gage slipped due to the gripping of the specimen, causing the measures of strain at the beginning of the test to be inaccurate. Since the Young modulus is calculated in the first part of the test (the elastic part of the stress-strain curve) the error of the strain gage measurements made the Young modulus incorrectly evaluated, with a value of 236.16 GPa, not corresponding to the expected values for cast irons. For that reason, we discarded the Young modulus calculated for the first specimen. The other measures of the first specimen, such as percent elongation, yield and ultimate stress were maintained as they do not depend on the strain gage data in the beginning of the test.
From the data acquired during the tests, we can draw stress-strain curves for the specimens, illustrated in Figure 3.5. The variability of the results visible in Figure 3.5, where we can also see the slip of the first specimen strain gage. The maximum elongation is about 4 %, indicating a brittle failure. Moreover, the average Young modulus of 177.67 GPa, yield stress of 400.02 MPa and ultimate stress of 708.11 MPa are all within the expected values for a cast iron. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Strain [%] 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 Stress [MPa ] Specimen #1 Specimen #2 Specimen #3 Specimen #4 Specimen #5 Specimen #6
Figure 3.5 – Stress-strain curves for the monotonic tensile test of the six specimens.
Lastly, we analyzed the fracture surface using the SEM and verified the chemical composition of the material. Since the SEM analyzed the monotonic and fatigue fractures at the same time, we will present the methodology and results of the microscope for both tests in a separate section.
3.2 Specimen tensile fatigue tests
The next step for the material characterization was testing the specimens under cyclic loading with the objective of identifying the fatigue limit for the cast iron used for the crankshaft samples and comparing them to the fatigue strength from crank throw tests, thus determining the effect of deep rolling. For the fatigue tests, we followed the ASTM E466-07 standard. This document provides information on specimen design and preparation, test equipment characteristics, control and termination. The same MTS test system of the monotonic tensile test was used.
The ASTM standard gives orientation on the maximum length of the test section in order to avoid buckling when in compression. However, the MTS system poses two limita-tions for the specimen design. First, there is a minimum specimen length of 60 mm for fatigue specimens, still larger than the maximum possible length for a circular specimen cut from the main journals. Second, the grips of the test system are worn out, so any compressive load would make the specimen slip and rotate, invalidating the test.
With those limitations in mind, we must re-evaluate the specimen design and test conditions. With the impossibility of using circular specimens, we must manufacture flat spec-imens, similarly to the tensile test. Moreover, the grip limitation under compression forces the load ratio of the fatigue test to R > 0. With no compression during the test, we do not need to worry about buckling. In conclusion, the use of flat specimens with no maximum test section length allows us to use the same specimens from the monotonic tensile test, as illustrated in Figure 3.2. The difference comes with the machining of the fatigue specimens, which accord-ing to the ASTM standard must be grinded and polished with a maximum surface roughness of 0.2 µm Ra. Figure 3.6 shows two specimens before and after the fatigue tests.
The MTS servo-hydraulic tested the specimens at 30 Hz with a load ratio of R = 0.1. For each specimen, we measured the cross-section area and specified the desired maximum stress. With that information, we calculated the maximum load to be controlled by the MTS. Given a load ratio, we then calculated the minimum load to be controlled as 10% of the maxi-mum load. Figure 3.7 is a screen shot of the controller’s oscilloscope showing the peak-to-peak load and displacement of the actuator for the first specimen. We will not show the oscilloscope screen of the other specimens as they are similar.
Each specimen was tested until complete failure and the number of cycles was reg-istered. The maximum load and stress, along with the specimen life are, shown in Table 3.4. The S-N curve is plotted in Figure 3.8. Again, for the fatigue tests we analyzed the fracture surface at the SEM, which we will discuss in detail in a separate section.
Since the stress ratio is R = 0.1 for the specimens and R = −1 for the crank throws, we need to find the equivalent fully reversed fatigue strength σf for the specimens, based on
Ad-(a)
(b)
Figure 3.6 – Fatigue tensile test specimen (a) Before the test; (b) After the test.
Table 3.4 – Fatigue tensile test life results for the six specimens Specimen # Thickness x
Width [mm] Max. Load [N] Max. Stress [MPa] Number of cycles
1 5.97 x 5.98 14280 400.00 192332 2 5.98 x 5.98 17880 500.00 27777 3 5.98 x 5.98 16680 466.44 18735 4 6.13 x 5.99 15480 421.58 82920 5 6.13 x 6.02 13838 375.00 414990 6 6.07 x 5.99 12726 350.00 799661
Figure 3.7 – Screen shot of the controller’s oscilloscope for the first specimen showing load and displacement of the actuator.
ditionally, we need to correct the results of axial fatigue strength to the bending, as discussed in Section 2.1, increasing the value of the calculated stress by 20%. Table 3.5 shows the mean and alternating components of the axial fatigue test loads, its corresponding σf using (2.6) and
the correspondent bending stress. We adopt the mean ultimate strength σut= 708.11 MPa from
Table 3.3. Based on that, we obtained the S-N curves for the axial fully reversed case and the equivalent bending fatigue strength, and plot these curves in Figure 3.8 with the original S-N curve.
Table 3.5 – Corresponding fully reversed fatigue strength of specimens using the modified-Goodman relation. All stresses are given in [MPa].
Specimen # σmax σmin σa σm Axial σf Bending σf
1 400.00 40.00 180.00 220.00 261.13 326.41 2 500.00 50.00 225.00 275.00 367.86 459.83 3 466.64 46.66 209.99 256.65 329.37 411.71 4 421.00 42.10 189.45 231.55 281.50 351.87 5 375.00 37.50 168.75 206.25 238.10 297.63 6 350.00 35.00 157.50 192.50 216.30 270.38
We were unable to test more specimens at lower stresses to obtain data for over one million cycles. Therefore, we must estimate high cycle data. We can see from the tendency line of the bending fully reversed case in Figure 3.8 that for the same loading case as the crank throw, the specimen has a fatigue strength for 2 million cycles of 224.67 MPa if we consider that the S-N curve maintains its behavior after one million cycles. If we consider that the material presents the endurance limit for one million cycles, than the fatigue strength is 256.12 MPa beyond that point. We will compare these results with crank throw fatigue strength obtained
104 105 106 Number of cycles 100 150 200 250 300 350 400 450 500 Stress amplitude [MPa ] Original set Fully reversed Bending y = -16.33ln(x) + 379.17 y = -36.29ln(x) + 706.34 y = -45.37ln(x) + 882.93 R2 = 0.9182
Figure 3.8 – S-N curves for the experimental set, corresponding fully reversed axial and bend-ing load cases.
from the resonant test rig in Chapter 7. From the difference between them, we will be able to evaluate the effect of fillet rolling on the fatigue strength of crankshafts.
3.3 Scanning Electron Microscope (SEM) Analysis
After the monotonic and fatigue tensile tests, we saved one specimen from each test to be analyzed in a Scanning Electron Microscope (SEM). Both samples were prepared in the same way. First, we cut a 10 mm piece from each specimen, polished the bottom to flatten the base surface and then put the samples in ultrasound to remove any impurity. Figure 3.9 shows a photograph of monotonic and fatigue tensile fractured specimens.
The SEM scans the surface by using a beam of electrons, which interact with the sample’s atoms, providing signals that gives information about the surface topology. The elec-tron beam can also ionize the atoms, which in turn emit X-rays. Each element emits X-ray at different energy levels, allowing us to identify the chemical composition of the samples by analyzing the X-ray energy. Specifically, the SEM used in this analysis employed an energy-dispersive X-ray spectroscopy (EDS) technique to obtain information of chemical composition. The analysis took place at the LRAC (Laboratório de Caracterização de Biomassa, Recursos Analíticos e de Calibração) of the School of Chemical Engineering (FEQ) at UNI-CAMP. The laboratory uses LEO Electron Microscopy/Oxford equipment, Leo 440i model for the SEM, equipped with a 6070 model EDS, shown in Figure 3.10. An acceleration tension of 20 kV and beam current of 600 pA were used.
Figure 3.9 – Samples after proper preparation for the SEM, cut from monotonic (left) and fa-tigue (right) specimens.
Figure 3.10 – Scanning Electron Microscope and energy-dispersive X-ray spectroscopy equip-ments.
3.3.1 Fracture surface analysis
Now we will show some of the images of the fracture surfaces obtained by the microscope. First we will analyze the monotonic tensile test specimen. Figure 3.11 shows pho-tographs with different magnitudes of enlargement, ranging from 53x to 1500x.
From the pictures of Figure 3.11 we can observe that the fracture is in fact brittle, with no cup and cone formation, with visible cleavage planes. This corroborates the conclusion of Section 3.1 that this is a cast iron with a brittle behavior.
Since we are analyzing a crankshaft material that should have more ductility than other types of irons (such as the grey iron, for example), we would expect this to be a nodular cast iron. One characteristic of nodular cast irons is the presence of graphite spheres, which in-hibits the creation of cracks, thus improving the ductility of this type of iron. Graphite spheres
