NUMERICAL ASSESSMENT OF THE MINIMUM DISTANCE BETWEEN HOLES IN 3D COMPONENTS AND EVALUATION OF THE USE OF TWIST DRILLS IN THE HOLE-DRILLING METHOD
Dissertação submetida ao Programa de Pós-Graduação em Engenharia Mecânica da Universidade Federal de Santa Catarina para a obtenção do Grau de Mestre em Engenharia Mecânica.
Orientador: Prof. Rolf Bertrand Schroeter, Dr. Eng.
Coorientador: Matias Roberto Viotti, Dr. Ing.
Florianópolis 2018
Special thanks to:
– PETROBRAS/CENPES for funding this work; – PRH-34/T3 Program, for providing the scholarship;
– I would like to express my gratitude to Prof. Rolf and Dr. Matias Viotti for their support, encouragement and valuable advices;
– The guidance provided by Prof. Rodrigo Blödorn and the countless discussions through video conference and face-to-face meetings throughout the development of this work fostered my professional and also personal growth;
–The friendship and collaboration of Prof. Denis and Célio at CTIF/UNIFEBE. Besides the time spent with the machining experiments at CTIF, Prof. Denis also helped with the Alicona measurements and his efforts to find out the source of data issues generated by limitations of the commercial software made the analysis feasible and pleasant;
– All the staff and my peers at LABMETRO and LMP, in special to Elsio, Michel and Janaina. Their trainings on using equipment and softwares were valuable to my professional growth;
– LABCONF, LABMAT, LCM and LCME for granting me access to the necessary equipment and the willingness to help and guidance provided by the staff;
– Sincerely thanks to Ph.D. candidate Sergio dos Anjos for his assistance and patience with the instrumented indentation tests performed at Laboratório de Metalurgia Física (LABMET/UNICAMP);
– The undergraduate interns I had the honor to work with: Edson, Lucas, Marcos and Felipe;
–My gratitude to Tecnotêmpera for their support with the stress relief heat treatment.
A indústria do petróleo e gás natural produz e distribui petróleo bruto e seus derivados, sendo parte destes produtos transportados por uma grande rede de oleodutos. Para prevenir falhas catastróficas é necessária a implementação de programas de manutenção preventiva que, em muitos casos, inclui a identificação do estado de tensões residuais para auxiliar na avaliação da resistência à fadiga. O Método do Furo Cego (MFC) é a técnica de medição de tensões residuais mais empregada para realizar medições em campo, e consiste na análise de deslocamentos e deformações resultantes do alívio de tensões promovido pela usinagem de um furo cego em um corpo. Normalmente, múltiplas medições são efetuadas para haver relevância estatística e, para a validação de diferentes técnicas, medições de tensão residual são realizadas diretamente em peças com perfil de tensões residuais conhecido, como o de peças jateadas. Pesquisadores do MFC costumeiramente também empregam dispositivos de carregamento para introduzir um estado de tensões residuais conhecido. Este trabalho busca investigar o uso de brocas helicoidais no MFC e realizar uma análise numérica do dispositivo de carregamento e da distância mínima entre os centros dos furos sob diferentes condições de carregamento. Primeiramente, tal dispositivo foi modelado e simulado em linguagem paramétrica (Mechanical APDL) e, na sequência, o modelo foi validado experimentalmente. Na parte experimental deste trabalho, o emprego de brocas helicoidais, comumente utilizadas na usinagem de furos, foi avaliado no âmbito do MFC. Realizaram-se pré-testes para identificar os danos gerados na subsuperfície da parede dos furos produzidos por brocas helicoidais com ângulo de ponta de σ=118º e σ=150º. Os seguintes materiais foram analisados: aço ABNT 1020, alumínio AA 6061 e aço inoxidável AISI 304L. Por último, avaliou-se a aplicabilidade de técnicas ópticas na medição de deslocamentos para as geometrias de furo obtidas sob dois estados de tensão: em placas jateadas com perfil de tensão compressivo e também com auxílio do dispositivo de carregamento que induz um carregamento de flexão. Identificou-se que a razão comprimento/largura da placa exerce forte influência sobre as tensões transversais introduzidas na placa. Em seguida, uma análise numérica da distância entre furos foi realizada em corpos de prova delgados e espessos considerando as tensões na borda do furo. Para o caso biaxial, o mais severo, uma influência de menos de 3% foi constatada para furos passantes com 4,5D (4,5 vezes o diâmetro) e 2,2D para corpos espessos. Através das análises metalográficas e medições de dureza foi possível constatar que os corpos
de usinagem devem ser escolhidos cuidadosamente a fim de evitar a introdução de riscos na superfície de referência devido às condições de formação de cavaco das brocas helicoidais. Nenhum tipo de cavaco favorável foi obtido para o aço inoxidável para as ferramentas testadas. Com base nas medições de tensões residuais, foi possível verificar que essas ferramentas possuem potencial para possível aplicação no MFC. Entretanto, melhorias na microgeometria do raio de gume, além da identificação de parâmetros de usinagem mais adequados e mudanças na relação de incremento no sentido de remover uma quantidade maior de material se fazem necessárias para que a utilização de brocas helicoidais no MFC possa se equiparar à técnica empregada atualmente. Os primeiros incrementos removem uma quantidade pequena de material, o que resulta em pequenos deslocamentos, sendo que o atual sistema óptico de medições não é capaz de capturar deslocamentos de tão baixa magnitude quando associados à presença de riscos na superfície de referência. Palavras-chave: Tensão residual. Método do Furo Cego. Brocas helicoidais. Análise de elementos finitos. Dispositivo de carregamento. Distância entre furos.
The oil and gas industry produces and distributes crude oil and its derivatives. An extensive pipe network transports part of these products. In order to prevent catastrophic failures, it is necessary to perform preventive maintenance programs that may include the evaluation of the stresses acting on the component. Knowing the residual stress state is of extreme importance in assessing the fatigue life of a component. The Hole-Drilling Method (HDM) is the most employed technique to perform in-field residual stress measurements. This method consists in analyzing the displacements/strains as a consequence of the stress relief generated by machining a blind hole in the workpiece. Usually, a few measurements are performed in order to infer about their statistic relevance. Residual stress measurements are performed in workpieces under a known stress profile, such as shot peened workpieces, in order to validate different techniques. In addition, HDM researchers commonly employ loading devices to induce a known residual stress state. This work aims to investigate the use of twist drills in the HDM and perform a numerical assessment of the loading device and the minimum distance between hole centers under different loadings conditions. First, such a device was modeled and simulated with a parametric language (Mechanical APDL). The model was validated with experimental measurements. In the experimental part of this work, the usage of twist drills, which are commonly employed to machine holes, was evaluated. Pre-tests were performed to identify the subsurface damage introduced by twist drills with point angle of σ=118° and σ=150° on the following materials: steel ABNT 1020, aluminum AA 6061 and stainless steel AISI 304L. The applicability of optical techniques to perform the displacement measurements with such a hole geometry produced by twist drills was also analyzed for both a compressive residual stress profile (shot peening) and flexural stresses induced with the aid of a loading device. It was identified that the length/width ratio of the plate strongly influences on induced transversal stresses. Then, a numerical analysis of the distance between hole centers was performed on thin and thick workpieces considering the stresses at the edge of the hole. For the biaxial case, which is the most severe one, an influence of less than 3% is obtained for through holes with 4.5D (4.5 times the diameters) and 2.2D for thick workpieces. The metallographic analysis and hardness measurements showed that considerable hardness increase was identified in the hole wall for the stainless steel and aluminum. Chip forming is a major issue and the parameters need to be carefully chosen in order to avoid scratching the
that these tools have the potential to be used in the HDM. However, improvements in the microgeometry of the cutting edge, optimization of cutting parameters as well as changes in the increment ratio in order to remove more material are necessary to narrow the performance gap between the proposed and the current technique. The first increments remove a small quantity of material, which induces small displacements. The current optical system is not capable of capturing such small displacements when associated with scratches on the reference surface. Keywords: Residual stress. Hole-drilling method. Twist drills. Finite element analysis. Loading device. Distance between hole centers.
Introdução
O Método do Furo Cego (MFC) consiste na medição dos deslocamentos/deformações geradas localmente no corpo de prova em função do alívio das tensões promovido pela confecção de um pequeno dano (furo) no componente. Tal furo é frequentemente produzido com auxílio de uma fresa de dentista (vulgo “broca de dentista”). Este método é amplamente utilizado para medição de tensões residuais em tubos como parte dos planos de manutenção preventiva que visam avaliar o estado de tensões em dutos que transportam petróleo e seus derivados. Em desenvolvimento há quase um século, diversos pesquisadores têm se dedicado a otimizar o processo de medição, tendo todo este esforço, inclusive, resultado na normalização do procedimento através da norma ASTM E837 – 13a. Para possibilitar a validação dos resultados, medições de tensão residual são comumente realizadas em corpos de prova com estado de tensão conhecido, sendo bastante utilizados também os dispositivos que induzem uma tensão conhecida no corpo de prova. Todavia, o MFC ainda possui limitações referentes à grande dificuldade de realização do furo em materiais de difícil usinagem, dado o rápido desgaste e eventuais quebras da ferramenta, além do fator limitante relacionado ao torque fornecido pelas furadeiras pneumáticas disponíveis no mercado.
Objetivos
Este trabalho é dividido em duas partes: experimental e de simulação. O objetivo da parte experimental é avaliar o emprego de brocas helicoidais com diferentes ângulos de ponta na medição de tensão residual pelo Método do Furo Cego com o auxílio do método óptico ESPI (Electronic Speckle Pattern Interferometry) para a medição dos deslocamentos. Já a parte numérica visa avaliar o comportamento de uma chapa fina sobre um dispositivo de flexão e identificar as distâncias entre furos mais apropriadas para o MFC em corpos de prova com diferentes geometrias e condições de carregamentos.
Para a avaliação do emprego de brocas helicoidais foram realizados pré-testes com o intuito de identificar os parâmetros de usinagem mais adequados para a realização das medições de tensão residual. Dado que para a utilização de técnicas ópticas a superfície de referência deve permanecer intacta durante a realização do furo, realizou-se a captação e análirealizou-se dos cavacos para cada parâmetro de usinagem testado durante os pré-testes. Utilizou-se um centro de usinagem Romi D 600 para a realização dos ensaios e, na sequência, as peças foram cortadas na seção transversal dos furos. Isto permitiu a identificação dos danos introduzidos durante a usinagem através da aquisição de micrografias e da realização de testes de indentação instrumentada. Os parâmetros mais adequados foram selecionados para a realização dos testes envolvendo a medição de tensões residuais em corpos de prova sob estados de tensão conhecidos: trativo (placa de flexão fixa sobre o dispositivo de flexão) e compressivo (placa jateada). Com relação à parte numérica, medições foram realizadas com o auxílio de um relógio comparador e do Microscópio de Foco Infinito da fabricante Alicona® para aferição da geometria antes e após o acoplamento da placa no dispositivo de flexão. Considerações no sentido de simplificar o dispositivo de flexão foram realizadas para viabilizar a modelagem do mesmo no software Mechanical APDL. Visando reduzir o custo computacional, adotou-se uma malha estruturada e considerou-se a base (dispositivo de flexão) como sendo um corpo rígido. Um estudo de malhas foi realizado para definir o tamanho dos elementos. Na sequência, o comportamento da placa na região de interesse foi comparado com medições experimentais. Os valores de tensão σx e σy foram comparados
com dados experimentais e teóricos encontrados na literatura. Por último, procedeu-se a uma análise detalhada da influência de um furo previamente existente sobre as tensões na borda do segundo furo para as seguintes condições de carregamento: placa sob estado de flexão, uniaxial e biaxial, sendo que para os dois últimos casos foi realizada uma análise complementar considerando uma placa espessa.
Resultados e discussões
A análise dos cavacos coletados durante os pré-testes mostrou que, para os parâmetros testados, cavacos favoráveis à utilização de técnicas ópticas para medição de deslocamento foram obtidos para a liga de aço ABNT 1020 e alumínio AA 6061. Porém, não foram identificados
deformação plástica introduzidos durante a usinagem, sendo que foram identificadas variações na espessura da região afetada apenas para o aço inoxidável AISI 304L em função do avanço. Um significativo aumento na dureza gerado em decorrência do processo de usinagem foi identificado, porém não foi possível identificar variação significativa da dureza em função dos parâmetros adotados. Problemas relacionados ao riscamento da superfície de referência foram enfrentados durante os testes realizados na placa sob flexão para a ferramenta com ângulo de ponta de σ=150°. Apesar das limitações de diâmetro apresentadas pelo sistema óptico, resultados compatíveis com os valores esperados foram obtidos para o corpo de prova com perfil de tensão compressivo (placa jateada). Já os testes realizados nos corpos de prova com perfil de tensão trativo apresentaram desvios maiores, principalmente para a ferramenta com ângulo de ponta de σ=150°. Estes desvios certamente surgiram em decorrência dos pequenos deslocamentos gerados durantes os primeiros incrementos, aliados aos riscos introduzidos na superfície de referência e à estreita região anular utilizada para a captação dos deslocamentos pelo interferômetro óptico.
O modelo numérico obtido possibilitou identificar o perfil de tensões ao longo da placa, que apresenta uma leve variação ao longo da largura e também do comprimento. Tal modelo foi comparado com dados experimentais e teóricos obtidos por outros pesquisadores. Verificou-se que há certa inconsistência entre o método apresentado na literatura para estimar as tensões em (y) e os valores obtidos numericamente. Estes valores são influenciados pela razão entre a largura e comprimento da placa (W/L). Para valores de W/L>1 as tensões na direção y na região central da placa se tornam constantes e próximas ao valor teórico. Além da verificação do valor das tensões, também verificou-se que o raio de curvatura anticlástica do modelo numérico é compatível com as medições realizadas experimentalmente. Para a placa contendo três furos e acoplada sobre o dispositivo de flexão, uma distância mínima de 3,0D resultou em variação nas tensões inferior a 3%. Para o estado uniaxial de tensão com furo passante, as distâncias de 2,25D (uniaxial) e 4,5D (biaxial) foram obtidas, enquanto que para furos cegos em placas espessas as distâncias mínimas apresentaram valores bastante reduzidos, da ordem de 1,5D (uniaxial) e 2,2D (biaxial).
contendo uma seção cônica) leva a uma redução no alívio das tensões, resultando em menores deslocamentos principalmente para os primeiros incrementos onde uma quantidade pequena de material é removida. Neste caso, as vantagens associadas ao aumento da estabilidade da quina da ferramenta (maior ângulo de quina) durante o processo de usinagem de materiais de difícil usinabilidade acarreta em redução da sensibilidade do processo de medição. Todavia, os testes realizados nos corpos de prova submetidos ao processo de jateamento – que não tiveram a superfície de referência danificada – mostraram que é possível obter uma boa estimativa do estado de tensão para esta geometria de furo através do método uniforme de medição de tensão residual.
Com relação às análises numéricas, obteve-se um modelo simplificado do dispositivo de flexão e pôde-se identificar a distribuição de tensões e a influência da razão W/L sobre estas tensões. Para o caso de furos passantes, o material presente ao redor do furo tem de suportar os esforços que atuavam no material removido durante o processo de furação. No caso de placas espessas, tanto o material ao redor do furo quanto abaixo dele ajudam a suportar as cargas, resultando na redução do alcance da variação de tensão ao redor do furo. Já para placas finas contendo furos cegos entra em cena o efeito de flexão que acaba influenciando os valores de tensão afetando, consequentemente, as distâncias entre furos.
Figure 1-1 – Hole geometry variation with point angle (σ). ...31
Figure 2-1 – Explosion caused by a pipeline failure. ...34
Figure 2-2 – Residual stress field divided into three categories: I, II and III. ....35
Figure 2-3 – Generation of micro- and macroscale residual stresses. ...36
Figure 2-4 – Specimen under tensile stress before and after the RS measurement. ...37
Figure 2-5 – Full-field ESPI data before and after the hole-drilling procedure in a workpiece under tensile residual stress. ...38
Figure 2-6 – Cutting parameters adequacy. For RS deviation higher than 60 MPa (High), lower than 30 MPa (Low), and the gray area lies between these values. ...40
Figure 2-7 – Cutting edge geometry. ...41
Figure 2-8 – Twist drill nomenclature (a) geometric parameters (b) and cutting speed (c). ...42
Figure 2-9 – Shear strength x strain diagram (a) and chip form (b). ...43
Figure 2-10 – Surface integrity and its layers. ...44
Figure 2-11 – Shear zones present in the machining process...46
Figure 2-12 – Typical stress distributions in manufacturing processes. ...47
Figure 2-13 – Distribution of micro-hardness HV0.1 after turning of C45 steel ...48
Figure 2-14 – Distribution of residual stress after turning of C45 steel ...49
Figure 2-15 – Radial section of the frictionally penetrated and thermomechanically affected aluminum AA-6061 (a) and microhardness profile (b) for the thermomechanically affected zone (TMAZ) and heat affected zone (HAZ). ...50
Figure 2-16 – HAZ generated on drilling of hardened steel. ...51
Figure 2-17 – Cutting edge temperature with number of passes (a), where rp=5 mm represents the peripheral position, and cutting temperature along the tool radius (b). ...52
Figure 2-18 – Temperature profile of a twist drill (a, b) and normalized temperature distribution (c). ...52
Figure 2-19 – Shape of commonly employed 3D elements. ...54
Figure 2-20 – Plate with a hole under uniform stresses. ...55
Figure 2-21 – Scheme of the anticlastic curvature. ...57
Figure 2-22 – Pure bending of plates. ...57
Figure 2-23 – Theoretical and experimental values (a) obtained on a residual stress test bench with four screws at the extreme ends (b). ...58
Figure 2-24 – Loading device with a slot machined out. ...59
Figure 2-25 – 4-point bending apparatus. ...60
Figure 2-26 – Stress concentration factor for equibiaxial, uniaxial and pure shear. ...61
Figure 2-27 – Stress concentration factor at a semi-finite plate as a function of the distance to the edge of the plate. ...61
Figure 3-1 – (a) Support developed to acquire SEM images of the twist drills. (b) Images of each tool, and (c) approximation of the hole geometry after each
increment. ... 66
Figure 3-2 – Illustration of the feed per tooth and tool edge radius ratio for ratio values of approximately 0.1 (a) and 1 (b). ... 67
Figure 3-3 – Workpiece clamping method and chip gathering. ... 68
Figure 3-4 – Process followed to acquire images of the transversal cross-section. ... 69
Figure 3-5 – Indentation scheme for σ=150°. ... 71
Figure 3-6 – Scheme of the ABNT 1020 specimens employed for RS tests. .... 73
Figure 3-7 – Loading device (a) and symmetry conditions and simplifications applied on the computational model (b) of the loading device. ... 73
Figure 3-8 – Experimental setup for the RS tests. ... 74
Figure 3-9 – Simplification of the loading device. ... 76
Figure 3-10 – Scheme of the measurement performed on the specimen. ... 77
Figure 3-11 – Illustration of the transverse curvature of the loading device... 77
Figure 3-12 – Bending apparatus and mounted plate measurements performed on three different plates. ... 78
Figure 3-13 – Comparison of the curvature radius of the loading device with the theoretical value (circle equation). ... 79
Figure 3-14 – Tetrahedral mesh generated for a ¼ model of the plate. ... 81
Figure 3-15 – Hexahedral mesh generated for a ¼ model of the plate and loading device. ... 82
Figure 3-16 – Normal vectors orientation of contact and target elements. ... 83
Figure 3-17 – Boundary conditions (a) and meshes generated (b) for the uniaxial and biaxial cases. ... 84
Figure 3-18 – Stress at the edge of the hole on a mounted plate for different mesh sizes. ... 85
Figure 4-1 – Transverse curvature of the plate at the center (Anticlastic curvature)... 87
Figure 4-2 – Theoretical and simulated stress values induced at the plate. ... 88
Figure 4-3 – Stress variation with plate width and plate length ratio at the center of the plate. ... 89
Figure 4-4 – Y-stresses and distance between the plate and upper curved surface of the loading device for two plate width/length ratios (1/4 model). ... 90
Figure 4-5 – Stress variation on the surface of the plate along plate width. ... 91
Figure 4-6 – Stress variation on the surface of the plate along plate length. ... 92
Figure 4-7 – Stress distribution along plate width for two holes. ... 93
Figure 4-8 – X-stress variation using the plate with a single hole at the center as a reference. ... 94
Figure 4-9 – X-stress variation using the plate without the central hole as a reference for points A and B, and with only one hole as a reference for point C. ... 95
Figure 4-11 – Influence of the distance between holes on the stress concentration at the edge of the hole. ...97 Figure 4-12 – Influence of the distance from the edge of the plate on the stress concentration at the edge of the hole. ...98 Figure 4-13 – Influence of the hole distance on stress concentration for a plate under biaxial load. ...99 Figure 4-14 – Influence of the distance from the edge of the plate on the stress concentration at the edge of the hole. ...100 Figure 4-15 – X-stresses for uniaxial and biaxial cases. ...101 Figure 4-16 – Steel ABNT 1020 chips for different point angles and cutting parameters. ...102 Figure 4-17 – Aluminum AA 6061 chips for different point angles and cutting parameters. ...103 Figure 4-18 – Stainless steel AISI 304L chips for different point angles and cutting parameters. ...104 Figure 4-19 – AISI 304L chip form for each repetition and final tool wear. ...106 Figure 4-24 – Hole bottom and wall for ABNT 1020 (vc=100 m/min, fz=10 μm). ...107 Figure 4-25 – Plastic deformation at the bottom of the hole for aluminum AA 6061. ...108 Figure 4-26 – Deformed layer at the hole bottom (slightly displaced from the center) for stainless steel AISI 304L and σ=118°. ...109 Figure 4-27 – Deformed layer at the hole bottom (slightly displaced from the center) for stainless steel AISI 304L and σ=150°. ...109 Figure 4-28 – Nanohardness values and micrographs for ABNT 1020 at the hole wall. ...111 Figure 4-29 – Nanohardness values and micrographs for AA 6061 at both hole wall and bottom center. ...112 Figure 4-30 – Nanohardness values and micrographs for AISI 304L at both hole wall and bottom center. ...113 Figure 4-31 – Nanohardness results for AISI 304L at different distances from the machined surface. ...114 Figure 4-32 – Interferograms acquired after the tenth increment (if not otherwise stated) on steel ABNT 1020. ...116 Figure 4-33 – Interferograms acquired after the tenth increment (if not otherwise stated) on steel ABNT 1020. ...117 Figure 4-34 – Residual stress measurements performed on a steel ABNT 1020 plate under bending...118 Figure 4-35 – Residual stress measurements performed on a steel ABNT 1020 plate under bending (without the third increment). ...119 Figure 4-36 – Interferograms acquired after the tenth increment on a shot peened steel ABNT 1020 plate. ...121 Figure 4-37 – RS measurements on shot peened specimens. ...122
Figure 4-21 – Etching performed on AISI 304L with nitric and chromic acids. ... 141 Figure 4-22 – Effect of the etching time on AISI 304L micrographs generated with nitric acid. ... 142 Figure 4-23 – Texture deterioration near the surface of the plate generated by etching of AISI 304L. ... 142
Table 3-2 – Acids commonly employed to etch aluminum and steels. ...70 Table 3-3 – Material properties and element types employed in the numerical analysis. ...80 Table 4-1 – Chip geometry evaluation for twist drills with different point angles. ...105
AA Aluminum alloy
ABNT Associação Brasileira de Normas Técnicas AISI American Iron and Steel Institute
APDL Ansys Parametric Design Language
CETIF Centro de Tecnologia e Inovação em Fabricação CNC Computerized numerical control
DC Direct current
DIC Digital Image Correlation
ESPI Electronic Speckle Pattern Interferometry FEA Finite element analysis
FEM Finite element method
FKN Normal stiffness factor
HAZ Heat affected zone
HDM Hole-Drilling Method
HSS High-speed steel
HV Hardness Vickers
ISO International Organization for Standardization LabMat Laboratório de Materiais
LABMET Laboratório de Metalurgia Física e Solidificação LABMETRO Laboratório de Metrologia e Automatização LCM Laboratório de Caracterização Microestrutural LCME Laboratório Central de Microscopia Eletrônica LABCONF Laboratório de Conformação Mecânica LMP Laboratório de Mecânica de Precisão
MFC Método do Furo Cego
MTRES Medição de Tensões Residuais
RS Residual Stress
SCF Stress concentration factor
SEM Scanning electron microscope
TMAZ Thermomechanically affected zone UFSC Universidade Federal de Santa Catarina UNICAMP Universidade Estadual de Campinas WEDM Wire electrical discharge machining
Capital Letters
B Clockwise angle from the x-axis to σ1
(maximum principal stress direction) [°]
D Tool diameter [mm]
E Young’s Modulus [GPa]
Hd Hole depth [mm]
Lb Distance between holes [mm]
Le Distance from the edge [mm]
P, Q, T Combination stresses [MPa]
Tp Plate thickness [mm]
Y Distance from the neutral axis [mm]
Lowercase Letters
a̅, b̅ Calibration constants [-]
ap Depth of cut [mm]
b Chip width [mm]
f Feed [mm]
fz Feed per tooth [μm]
h Chip thickness [mm]
n Rotational speed [rpm]
p, q, t Combination strains
rp Peripheral position [mm]
vc Cutting speed [mm/min]
ve Effective cutting speed [mm/min]
vf Feed speed [mm/min]
z Number of teeth [-]
Greek Letters
α Clearance angle [°]
αn Tool normal clearance angle [°]
β Wedge angle [°]
γ Rake angle [°]
γn Tool normal rake angle [°]
εr Tool included angle [°]
ε1, ε2, ε3 Strains measured with strain gages [-]
η Effective cutting angle [°]
κr Cutting edge angle [°]
ρc Curvature radius [mm]
ρc′ Anticlastic curvature radius [mm]
INTRODUCTION ... 29 STATE OF THE ART ... 33 2.1 RESIDUAL STRESSES ... 33 2.1.1 Residual stress types ... 34 2.1.2 Hole-Drilling Method ... 36 2.1.3 Main factors influencing the Hole-Drilling Method ... 39 2.2 MACHINING ... 40 2.2.1 Drilling... 41 2.2.2 Influences on chip formation ... 43 2.2.3 Surface aspects and integrity ... 44 2.2.4 RS and hardness variation introduced by machining ... 45 2.2.5 Cutting temperature in the drilling process ... 51 2.2.6 Tool wear ... 53 2.3 FINITE ELEMENT METHOD ... 53 2.3.1 Calibration coefficients ... 54
2.4 MECHANICAL BEHAVIOR OF BEAMS UNDER BENDING
AND PLATES WITH HOLES ... 55 2.4.1 Anticlastic curvature ... 55 2.4.2 Loading devices ... 58 2.4.3 Stress concentration around holes ... 60 EXPERIMENTAL PLANNING... 65 3.1 PRE-TESTS ... 68 3.1.1 Nanohardness ... 71 3.2 RS TESTS ... 72 3.2.1 Specimens for RS tests ... 72 3.2.2 Loading device ... 73 3.2.3 Experimental setup for the RS tests ... 74 3.3 SIMULATION GUIDELINE ... 74 3.3.1 Boundary conditions ... 75 3.3.2 Characterization of the loading device ... 76 3.3.3 Element type and material properties ... 79 3.3.4 Meshing the plate and the loading device ... 81 3.3.5 Uniaxial and biaxial cases ... 83 3.3.6 Mesh convergence study ... 84 RESULTS AND DISCUSSIONS ... 86 4.1 EVALUATION OF THE NUMERICAL MODEL ... 86 4.1.1 Transverse curvature radius ... 86 4.1.2 Case study: loading device employed by Schajer [53]... 87
4.2 DISTANCE BETWEEN HOLES ... 92 4.2.1 Thin case (loading device) ... 92 4.2.2 Three holes on the plate ... 93 4.2.3 Thin, intermediate, thick cases (uniaxial, biaxial) ... 96 4.3 EVALUATION OF BLIND HOLES ... 101 4.3.1 Chip analysis ... 101 4.4 SURFACE INTEGRITY ANALYSIS ... 106 4.4.1 Identification of deformed layers ... 106 4.4.2 Nanohardness analysis ... 110 4.5 RS MEASUREMENTS ... 115 4.5.1 RS measurements on the loading device ... 115 4.5.2 RS measurements on a shot peened plate ... 120 CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK ... 123 5.1 CONCLUSIONS ... 123 5.2 SUGGESTIONS FOR FUTURE WORK ... 124 REFERENCES ... 127 APPENDIX A – CUTTING PARAMETERS ... 133 APPENDIX B – MEASUREMENT OF THE LONGITUDINAL CURVATURE RADIUS OF THE LOADING DEVICE ... 134 APPENDIX C – STRESS VARIATION FOR TETRAHEDRAL AND HEXAHEDRAL MESH ... 135 APPENDIX D – MEASUREMENTS OF THE TRANSVERSAL CROSS-SECTIONS ... 137 APPENDIX E – BURR FORMATION ... 139 APPENDIX F – ACQUISITION OF THE METALLOGRAPHIC PARAMETERS ... 140
APPENDIX G – RESIDUAL STRESS MEASUREMENTS:
COMBINATION STRAINS p, q AND t ... 143 APPENDIX H – AREAS OF DATA ACQUISITION ... 146
INTRODUCTION
The evaluation of the fatigue life or simply the improvement of the material resistance requires knowledge about the stress distribution and its magnitude. The stress distribution in a component is a combination of residual stresses and workloads. Residual stresses are introduced either accidentally or intentionally. They are sometimes unintentionally generated by a variety of manufacturing processes commonly employed in the industry. Residual stresses can be either tensile or compressive. Compressive residual stresses can be intentionally introduced to components throughout processes such as heat treating and shot peening, or even in manufacturing processes aiming the controlled introduction of these stresses.
The accidental introduction of residual stresses may also lead to tensile states, resulting in a lower mechanical strength or/and a shorter fatigue life. Therefore, the intentional introduction of residual stresses is usually limited to a compressive profile, consequently increasing the mechanical resistance and the fatigue life. This usually leads to a change in the elastic behavior of the material at the surface, disfavoring crack nucleation. The determination of residual stresses with analytical methods is considered, in most cases, a difficult task to perform. As a consequence, experimental methods are widely employed to measure residual stresses in industrial and laboratory environments [1]. It is well accepted in the literature that tensile residual stresses have a negative influence on some functional aspects, whereas compressive residual stresses present a favorable condition to these aspects [2]. The drilling process itself generates machining-induced residual stresses that alter the final results measured by the Hole-Drilling Method (HDM) [3–5].
The Hole-Drilling Method is a widely employed technique for residual stress measurement. It is suitable for many applications and has standardized procedures, resulting in good precision and reliable results. Even though a damage is introduced in the test specimen during the measurement procedure, in many cases it is possible to tolerate the harm caused to the component. For this reason, the HDM is considered a semi-destructive method [6]. Semi-semi-destructive techniques belong to an intermediate classification between non-destructive techniques such as X-ray diffraction and destructive techniques such as the Sectioning Method. Sectioning has a mechanical nature and may partially or totally affect the workpiece [1].
The HDM has its standard procedures presented in ASTM E837 – 13a [7]. The hole is made on the workpiece to produce a localized stress
relief, allowing the material to deform and equilibrate itself again. The stresses associated with this deformation are calculated according to the Hooke’s Law. These measurements are sensitive to the drilling process due to the residual stresses introduced by the machining process [5].
Much research has been performed on the influence of the distance between holes on the stress concentration of through holes on thin plates. However, to the best of the author’s knowledge, no investigation of blind holes has ever been performed. Nowadays, HDM researchers rely on theoretical results obtained for through holes on thin plates. The first section of this work is comprised of an investigation of the distance between holes and plate thickness for a plate under bending, uniaxial and equibiaxial stress. The influence of the distance between holes on the stresses and deformations around the blind hole is investigated with the aid of a finite element software. The restrictions imposed by the test specimen geometry motivated the numerical study to identify the most suitable distance between holes to perform the experiments. Blind holes under bending as well as uniaxial and biaxial loads are analyzed. In addition, the influence of the distance between the hole and the edge of the plate will also be addressed.
Twist drills are widely used nowadays and are the most employed tool to drill cylindrical holes [8, 9]. Twist drills present more favorable machining conditions and bigger flutes to remove the chips than end mills do. The usage of conical holes in the HDM produced with twist drills will be investigated in this work. On the second section of this thesis, the viability of twist drills will be analyzed. Twist drills with two different point angles and different machining parameters are employed to machine three different materials: AISI 304L, AA 6061 and ABNT 1020. The point angles employed in this study result in a hole geometry considerably different from what is presented in the standard, as shown in Figure 1-1. First, an analysis of the chip form and the damage introduced by each cutting parameter is presented. The subsurface damage is analyzed with the aid of micrographs of the hole cross-section and instrumented hardness measurements. Then, the best configuration is employed to perform residual stress measurements in steel ABNT 1020 under tensile stresses (loading device) and compressive stresses (shot-peened plate).
Figure 1-1 – Hole geometry variation with point angle (σ).
Source: the author.
This work is a result of a cooperation between the Precision Engineering Laboratory (Laboratório de Mecânica de Precisão – LMP/UFSC) and the Metrology and Automatization Laboratory (Laboratório de Metrologia e Automatização – LABMETRO/UFSC). The project was funded by PETROBRAS. Besides the aforementioned laboratories, the infrastructure of other research centers was employed in this study: Centro de Tecnologia e Inovação em Fabricação (CETIF/UNIFEBE), Laboratório Central de Microscopia Eletrônica (LCME/UFSC), Laboratório de Caracterização Microestrutural (LCM/UFSC), Laboratório de Conformação Mecânica (LABCONF), Laboratório de Materiais (LabMat/UFSC) and Laboratório de Metalurgia Física (LABMET/UNICAMP).
This thesis is divided in the following items:
Chapter 1: Introduction – Context, motivation, objectives, and organization of the document;
Chapter 2: State of the art – Background and literature review on the main content pertinent to the topic under investigation;
Chapter 3: Experimental planning – The methodology is thoroughly discussed in this chapter;
Chapter 4: Results and discussions – results obtained with the proposed analysis (numerical and experimental) are presented and discussed;
Chapter 5: Conclusions – the main conclusions drawn from this work are summarised and suggestions for future work are also presented in this chapter.
STATE OF THE ART
In this chapter, the current state of the art about the Hole-Drilling Method and machining will be presented. An overview of the main factors that influence on residual stress measurements and the introduction of residual stresses by machining process will be shown. In addition, a succinct review of the finite element method and the stress concentration around holes closes this chapter.
2.1 RESIDUAL STRESSES
Residual stress (RS) is defined as the stress state of a material which is not under the effect of an external force, such as gravity, or any other source of mechanical stresses like temperature gradients [6, 10]. In a similar way, the glossary of terms of the Mechanical Engineer’s Data Handbook [11] defines residual stresses as follows: stresses acting in a body free of external forces or thermal gradients. Residual stresses generated by small temperature gradients are transient and disappear after the temperature equilibrium is achieved if the residual stress does not surpass the yield strength [6, 10]. These residual stresses can also be added or subtracted from the load externally applied on the body. The stress combination can lead to dangerous situations when the residual stresses are not known [12]. Thus, evaluating the extent and direction of these stresses is relevant in engineering [13].
The composition of residual stresses with the working load can surpass the material yield stress, resulting in a catastrophic failure of the component [14]. Alone or in combination with other factors, residual stresses have already caused the failure of huge mechanical structures, such as bridges, airplanes, and ships, as well as small structures and equipment, resulting in the loss of many lives [6]. Figure 2-1 shows an example of a pipeline failure as a result of the combination of residual stresses and the working load associated with corrosion (typical stress under corrosion failure). Studies to map the residual stress state in pipelines is an effective way to prevent failures and an important part of predictive maintenance and fitness for service programs with periodic monitoring of residual stresses.
Figure 2-1 – Explosion caused by a pipeline failure.
Source: Ferreira [15].
Residual stresses are introduced in most manufacturing processes and, therefore, predicting them with confidence once the product is finished is certainly a difficult task. In addition, residual stresses may subsequently vary along the service life of the mechanical part [6, 7, 12]. 2.1.1 Residual stress types
Residual stresses can be classified according to the length necessary to cancel them out. They are usually classified into three categories [6, 10, 12]:
Type I: it is related to macroscopic dimensions and may extend to distances larger than 1 mm, represented by σI in Figure 2-2. This type
of residual stress is commonly found in manufactured products such as rolled plates;
Type II: microscopic residual stresses that extend over the micrometer range, such as the grain boundary interface (σII in Figure 2-2);
Type III: residual stresses that take place in the nanometer scale around the atomic plane displacements (σIII in Figure 2-2).
Figure 2-2 – Residual stress field divided into three categories: I, II and III.
Source: Abboud [16].
Some processes that commonly introduce micro- and macroscale residual stresses are presented in Figure 2-3. As an example, the work hardening generated by shot peening tends to displace the deformed layer horizontally. However, the displacement is retained to a certain extent by the tensile stresses located underneath the plastically deformed layer. As a result, a compressive profile is generated in the surface, while tensile stresses are created deeper into the workpiece to equilibrate the compressive stresses [6].
There is a wide variety of methods employed nowadays to measure residual stresses. The resolution, physical limitation, cost associated with the equipment, and the classification into non-destructive, semi-destructive and semi-destructive are the main criteria employed to choose the most suitable method.
Figure 2-3 – Generation of micro- and macroscale residual stresses.
Source: Withers and Bhadeshia [17].
Non-destructive methods usually require comprehensive calibration specific to each material type, while destructive and semi-destructive usually require less specific calibration – the latter measures either displacements or strains, which are fundamental quantities [18]. Besides the HDM, there are quite a few examples of relaxation measurement methods: the slitting method, the splitting method, the sectioning method, and the layer removal method. Another group of residual stress measurement methods are the diffraction methods (these methods allow non-destructive measurements): X-ray diffraction, synchrotron x-ray, and neutron diffraction. The x-ray diffraction method is commonly employed as a reference method when evaluating relaxation measurement methods. As this work deals with the HDM, in the next section a general view about the HDM will be presented.
2.1.2 Hole-Drilling Method
In 1934, Mathar pioneered the measurement of residual stresses in a single direction by identifying the displacement of symmetric regions around a hole before and after drilling [13]. Many researchers have worked to improve the HDM accuracy ever since, dealing with empirically or analytically obtained relationships between measured strains and residual stresses. In 1981, Schajer [19] first introduced the
Finite Element Method (FEM) into the technique to relate strains with stresses – commonly addressed to as Calibration Coefficients, opening a whole range of possibilities regarding the hole geometry. Shortly after that, Flaman [3] first employed high-speed turbines and obtained consistent results for hardening-sensitive materials. This was considered a stress-free technique and is still widely employed nowadays. The basic procedures for the Hole-drilling Method are presented in the standard ASTM E837 -13a [7], which references some authors that have contributed to the HDM.
The method is widely employed to measure residual stresses near the surface of linear-elastic materials. Either a small and shallow blind or a through hole is machined, usually with the aid of pneumatic air turbines, generating a stress relief around the hole, as shown in Figure 2-4. Hooke’s law states that strains and stresses are linearly related in the elastic region for the majority of engineering materials [20], allowing the computation of the stresses from the strains measured with strain gauges. Although the standard ASTM E837 -13a [7] only addresses the strain gage hole drilling, which is currently the most employed variant [13], in the last few decades many research centers have substituted strain gages by optical techniques such as Digital Image Correlation (DIC), Electronic Speckle Pattern Interferometry (ESPI) and Moiré Interferometry [6, 21, 22]. Figure 2-4 – Specimen under tensile stress before and after the RS measurement.
Optical techniques allow the acquisition of full-field data, covering a greater region and increasing, consequently, the data processing capability. In addition, ESPI uses a video camera enabling the visualization of live fringe patterns by image subtraction [6, 24]. Figure 2-5 shows a schematic comparison of the strain gage method with full-field techniques and the fringe pattern generated after drilling the hole. This fringe pattern is obtained by processing the first specklegram acquired before the perturbation (drilling) and the second one acquired after drilling. By applying a data processing technique the fringe pattern provides the approximate surface deformation. ESPI can measure displacements with precision up to a fraction of a micrometer.
Figure 2-5 – Full-field ESPI data before and after the hole-drilling procedure in a workpiece under tensile residual stress.
Source: adapted from Schajer [6].
The speckle pattern shown in Figure 2-5 is obtained by illuminating a rough surface with laser illumination (coherent light), which produces a granular pattern with high contrast and fine scale. This random distribution of scattered light is known as the ‘speckle effect’. Changes in the observation geometry and illumination, as well as laser light wavelength generated by temperature variation, among other factors, are able to modify the random distribution. Hence, extensive research
efforts were performed in the past to enable the measurement with high-accuracy of features of the surface such as components of the in-plane deformation [25].
2.1.3 Main factors influencing the Hole-Drilling Method
There is a series of steps that must be followed in order to ensure certain accuracy for residual stress measurements [7]. According to Flaman [3, 26], the most important factor to be considered when drilling a hole for the HDM is its final geometry and the introduction of additional stresses in the workpiece under investigation, generated by the machining process. Yielding of the material at the tool-workpiece interface and the resulting plasticity effects were pointed by Steinzig et al. [4] as possible explanations to the deviation from the real residual stress values, but he attributed the main cause of the stress variation to the degradation of the hole geometry.
Rotational speed is also one of the main concerns regarding the machining of materials with high strain-hardening sensitivity. A few authors have studied the effect of rotational speed on machining-induced residual stresses. The gap between the two rotational speeds (1 000 rpm and 400 000 rpm) investigated by Flaman in 1982 [3] was further analyzed by Steinzig et al. [4] and Tamura [5], showing promising results with rotational speeds in the order of 10 000 rpm – 25 000 rpm, which are a way lower than the rotational speeds commonly employed by the HDM nowadays, which was previously suggested by Flaman.
Table A-1 in APPENDIX A shows a compilation of the cutting parameters for stainless steel employed by HDM researchers [3–5, 27]. The influence of the feed rate and cutting speed is constantly studied by manufacturing engineers to evaluate the introduction of machining-induced residual stresses [2, 28], while the term ‘rotational speed’ is constantly employed by HDM researchers. However, the actual cutting speed is linked to the tool radius, which may lead to misinterpretation of the machining parameter. Thus, the term ‘cutting speed’ is preferred and will be employed throughout this document. The cutting speed and the feed rate were calculated for the aforementioned data to show the suitability of these parameters (Figure 2-6) in performing RS tests.
Figure 2-6 – Cutting parameters adequacy. For RS deviation higher than 60 MPa (High), lower than 30 MPa (Low), and the gray area lies between these values.
Source: [3–5, 27]. 2.2 MACHINING
Machining is by definition the cutting process in which layers are mechanically removed from the workpiece with the aid of a cutting tool. The removed material, commonly referred to as chips, may acquire a variety of shapes according to the cutting process, which can be classified as machining with geometrically defined and not defined cutting edges. This work concerns the use of twist drills and, therefore, special focus is given to geometrically defined tools. The basic geometry of the cutting part of a cutting tool is defined by the following parameters [8, 29]: Rake face: the surface over which the removed material flows as it is
removed. The rake angle (γ) is between the rake face and the plane normal to the cutting direction.
Flank face: it is turned towards the freshly generated surface and is defined by the clearance angle, shown in Figure 2-7. The clearance angle (α) is between the cutting direction plane and the flank face. Cutting edge: represents a smooth transition between the rake and
flank faces, either rounded or chamfered.
Wedge angle (β): the angle formed between the aforementioned faces.
Figure 2-7 – Cutting edge geometry.
Source: Whyen [29]. 2.2.1 Drilling
Drilling is a machining process in which one feed direction along the tool axis is combined with the main rotary motion [26, 28, 29]. This can be performed by a variety of tools, such as drills and end mills. Some variations such as profile center drilling, tapping, reaming and counterboring were developed to satisfy some requisites related to the material removal rate, dimensional precision, and surface quality. Twist drills are the most employed tools among the variations of the drilling process [26, 28].
Drills are commonly employed in roughing operations. The process has some peculiarities: a) variable cutting speeds (Figure 2-8c) which promotes, in some cases, the formation of build-up edges along the tool radius, b) effective cutting speeds near zero at the center, c) difficult chip removal, d) friction of the guide flutes against the hole wall, e) unfavorable heat distribution and increased wear [8]. In cases where accuracy and good finish are required, the operation is followed by reaming, boring, honing or grinding [30, 31].
The main elements that compose a twist drill are presented in Figure 2-8a, together with the main parameters representing the cross-sectional area of the undeformed chip (Figure 2-8b), which is the most influential factor on the cutting forces generated in the drilling process. The chisel edge presented in Figure 2-8c usually presents a highly negative rake angle and, therefore, rarely separates the material. Instead, it deforms and directs the material to the cutting edge [8].
The effective cutting speed (ve) is formed by the cutting speed (vc)
and the feed speed (vf), as shown in Figure 2-8c. The effective cutting
speed angle (η) represents the small variation between the effective cutting direction and the cutting speed direction.
Figure 2-8 – Twist drill nomenclature (a) geometric parameters (b) and cutting speed (c).
(a) (b) (c)
Source: adapted from Boeira [32]. Where:
φ = Helical angle;
κr = Tool cutting edge angle;
εr = Tool included angle.
The cross-sectional area A (Figure 2-8) is obtained multiplying the depth of cut (ap) by the feed per tooth (fz), as represented in Eq. (2-1) :
A = fz. ap= b. h (2-1)
Another possibility is to calculate the chip thickness (h) and chip width (b) with the point angle (σ) as shown in Eq. (2-2) and Eq. (2-3):
h = fz. sin (
σ
2) (2-2)
b = ap
sin (σ2) (2-3)
The cutting speed (vc), which usually relates to the cutting speed at
the tool diameter (D), is calculated with Eq. (2-4), where the rotational speed is represented by (n). Lastly, the feed per tooth (fz) is calculated
with Eq. (2-5), as well as the feed speed (vf) with Eq. (2-6), where (z)
represents the number of cutting edges. vc= π. D. n 1000 (2-4) fz= f z (2-5) vf= n. z. fz (2-6)
2.2.2 Influences on chip formation
The smaller the rake angle, the higher the degree of deformation, and consequently cutting forces and heat generation increase. This affects the chip form, as shown in Figure 2-9. For a twist drill, the rake angle varies with the tool radius, resulting in different degrees of deformation. This promotes the generation of different chip forms along the cutting edge on a single machining test. The amount of heat generation through friction and deformation, as well as the cutting parameters and tool geometry also influence on chip formation [8, 32].
Figure 2-9 – Shear strength x strain diagram (a) and chip form (b).
2.2.3 Surface aspects and integrity
Machined surfaces have two important aspects: surface texture and surface integrity. The former makes reference to geometrical irregularities, while the latter includes chemical, mechanical, thermal and metallurgical alterations in the outer surface layer. This layer is located right below the visible surface and commonly has its property variation identified by hardness variation, plastic deformation, and heat affected zones, as shown in Figure 2-10. The physical properties of the outer layer are altered as a result of the pressure generated by friction and cutting forces, distinguishing it from the base material. The general grain orientation pattern generated by the cutting force is represented in Figure 2-10 as the worked layer [9].
Figure 2-10 – Surface integrity and its layers.
Source: adapted from Davim [33].
It is not possible to clearly define the layers presented in Figure 2-10 [8]. In addition, these layers are usually classified in internal – worked and bulk material – and external layers. The internal boundary remains with the same chemical composition as the bulk material. On the other hand, the oxide layer is formed on the external layer shortly after the surface is machined with its first contact with the environment. The
adsorption layer is formed when the oxide layer is in contact with gases and water, creating the adsorption layer. Machining with coolants will also create a grease and oil film on top of the above-mentioned layers.
The characteristics of the worked layer depend basically on two factors: the material properties and the manufacturing operation [8]. Moreover, the surface structure – not restricted to the worked layer – may change during the service life. One example of this change is the severe plastic deformation identified on the surface layer of rails generated by the excessively high normal pressure and shearing [34].
The physical and mechanical alterations of the worked layer are commonly evaluated by the strain-hardening effect, induced residual stresses, as well as fracture mechanical testing and texture investigation [26, 34]. One example of this alterations occurs in steel processing under high temperatures and cooling rates, which may contribute to the development of a hardening zone in the outermost layer of the workpiece [8].
The theoretical roughness of the machined surface can be predicted by equations as a function of feed rate and edge radius. However, a series of negative effects distort the real surface roughness. These are some of the main factors that contribute to the deviation in the surface texture: spring-back effect, build-up edge, roughness along the cutting edge, inaccurate movements performed by the machine tool as a result of the bearing clearance effect, dynamic stiffness and feed control [28, 35]. 2.2.4 RS and hardness variation introduced by machining
Residual stresses appear as an elastic response to an incompatible local deformation within a component [6]. For instance, non-uniform plastic deformation forces the material to deform elastically to preserve its continuity, resulting in residual stresses. The following mechanisms contribute to generating residual stresses:
Non-uniform plastic deformation: it occurs in manufacturing processes such as forging, rolling and extrusion, where a shape variation takes place;
Surface modification: it occurs in manufacturing processes such as grinding and peening, as well as under working conditions by corrosion;
Phase transformation and/or material density that is commonly presented in processes involving high-temperature gradients: it occurs in manufacturing processes such as welding, forging and
quenching. The incompatibility generated between the affected surface and the underlying material results in residual stresses [16].
In machining, the deformation that occurs in the tool-workpiece interface can be divided into three shear zones, as shown in Figure 2-11. For the primary shear zone, most of the plastic deformation occurs and the chip is separated from the workpiece. For the secondary shear zone, the chip slides over the tool rake face. Finally, for the tertiary shear zone, the tool flank rubs against the surface generated by the chip removal. Heat is generated by friction in these zones and from plastic deformation. As the tool wear increases, the cutting edge radius and the rubbing increase, affecting the surface integrity [36].
Figure 2-11 – Shear zones present in the machining process.
Source: (a) Abboud [16] and (b) Klocke [8].
Residual stresses are inevitable consequences of the thermomechanical processing of steels [37]. Machining processes such as milling and turning remove a thin layer of material in the form of chips through plastic deformation, which are typical thermomechanical processes [16]. The resulting stress profile is usually non-uniform and presents high gradients due to the decreasing thermomechanical load with the increase of depth. Figure 2-12 presents the magnitude and typical stress distribution for three different types of manufacturing process, for a steel with yield strength of 650 MPa. The manufacturing processes usually introduce high peaks of residual stresses within short distances, resulting in steep gradients.
Figure 2-12 – Typical stress distributions in manufacturing processes.
Source: Totten et al. [37].
Stephenson and Agapiou [31] suggest that the following are the best approaches to decrease the generation of machining-induced residual stresses: (a) reducing the cutting speed, (b) increasing the clearance angle, (c) the use of coolant and (d) avoiding the use of worn tools. These changes result in lesser plastic deformation and heat generation by friction, as well as smaller temperature gradients at the cutting interface.
Grzesik and Żak [28] analyzed the surface integrity generated by oblique turning with negative rake angles of iron-based materials, including steel C45. It was found that the micro-hardness profile roughly coincides with the thickness of the surface layer in Figure 2-13(a). Negative rake angles, together with small minimum undeformed chip thickness, are expected to produce compressive residual stresses near the surface. By varying the cutting speed and feed rate, a 3D graph was obtained with the depth of the strain-hardened layer, as shown in Figure 2-13 (b), exhibiting which parameters presented the highest and smallest deformed regions.
Figure 2-13 – Distribution of micro-hardness HV0.1 after turning of C45 steel (vc=245 m/min, f=0,34 mm/rev, ap=0,5 mm, γn=-20º, αn=10º) and micrograph showing plastic deformation of the sub-surface region (a) and depth of strain-hardened layer (γn =-15º, αn=10º) (b).
(a) (b) Source: Grzesik and Żak [28].
The residual stresses were also measured presenting compressive values distributed along the thickness according to a parabolic profile. The maximum residual stresses as a function of cutting speed and feed rate, as well as the depth of the residual stresses profile are shown in Figure 2-14 [28]. Capello [2] also found that for steels including C45, the feed rate was the most influential factor followed by the nose radius, while keeping the cutting speed constant at 120 m/min. In this case, working with a commonly employed rake angle of γ=6°, tensile residual stresses in the range of 100-600 MPa were found. Saoubi et al. [38] found that machining-induced residual stresses slightly increase with cutting speed for AISI 316L, whereas the tensile layer depth reduces considerably. Increasing the feed rate also led to an increase in the tensile layer depth, but it had little influence in the stress magnitude. It was also identified that increasing the tool-edge radius leads to higher tensile residual stresses when machining AISI 316L,which was later confirmed numerically [39].
Figure 2-14 – Distribution of residual stress after turning of C45 steel
(vc=245 m/min, f= 0,34 mm/rev, ap=0,5 mm, γn= -20º, αn= 10º) (a) and depth of strain-hardened layer (γn= -15º, αn= 10º) (b).
(a) (b)
Source: Grzesik and Żak [28].
Min et al. [40] analyzed the microstructure of an AA 6061-T6 aluminum sheet frictionally penetrated by a rotating blind rivet. The thermomechanically affected zone presented a thickness of less than one millimeter, and pointed to a slight increase in the material hardness. In this case, the heat generated is extremely high, and the heat-affected zone extends at a radial distance for over four millimeters as identified by hardness tests, shown in Figure 2-15 (b). The heat-affected zone clearly goes beyond the deformed regions represented by zone A and B. Zone X, which has not been deformed, had its hardness affected by the heat generated in the process.
Figure 2-15 – Radial section of the frictionally penetrated and thermomechanically affected aluminum AA-6061 (a) and microhardness profile (b) for the thermomechanically affected zone (TMAZ) and heat affected zone (HAZ).
(a) (b) Source: Min et al. [40].
Smith (1989) apud Stephenson and Agapiou [31] analyzed holes produced on hardened steel (AISI 52100, 60 HRC). The machining process reached the austenite temperature for a short period of time, resulting in structural changes – generation of white layer or unetchable structure. The cutting of the point, as well as the rubbing action along the margins, generated heat, which contributes to the microstructural changes. The tool itself removes part of the HAZ generated as it is driven into the workpiece, but it remains in some locations as shown in Figure 2-16. Hardness tests showed the existence of a untempered martensite followed by a tempered martensite layer.
Figure 2-16 – HAZ generated on drilling of hardened steel.
Source: Smith (1989) apud Stephenson and Agapiou [31]. 2.2.5 Cutting temperature in the drilling process
Ueda et al. [41] measured the temperature at the cutting edge of a 10 mm cemented carbide drill with two flutes in four points along its radius with the aid of a pyrometer. It was found that the temperature at the cutting edge increases at the beginning of the machining process, and its increasing rate decreases with pass number, as shown in Figure 2-17a, taking longer to achieve a high constant temperature in comparison to other cutting processes such as turning. The same measurement was performed along the tool radius, showing a temperature increase as the cutting speed or tool radius increases (Figure 2-17 b). DeVries [42] also measured the cutting edge temperature of twist drills and found increasing temperatures with the increase of tool radius position. Watanabe (1977) et al. apud Bono and Ni [43] obtained a nearly constant temperature profile along the tool radius.
Figure 2-17 – Cutting edge temperature with number of passes (a), where rp=5 mm represents the peripheral position, and cutting temperature along the tool radius (b).
(a) (b) Source: Ueda et al. [41].
On the other hand, authors such as Bono and Ni [43] argued that the maximum temperature does not occur on the outer corner of the drill, but on the chisel edge, and it decreases as the radius increases, based on simulations and experimental results obtained by drilling aluminum 319 with a 10 mm HSS twist drill. Moreover, with the aid of a Scanning Electron Microscope (SEM) to analyze the microstructural changes on a 10 mm M2 HSS twist drill, it was found that the highest temperature was achieved at the tool tip when machining stainless steel with aggressive cutting parameters [44]. Figure 2-18 shows the temperature profiles in a twist drill, numerically obtained by different authors.
Figure 2-18 – Temperature profile of a twist drill (a, b) and normalized temperature distribution (c).
Source: (a) Li and Shih [45], (b) Thakur and Gangopadhyay [46] and (c) Bono and Ni [43].
2.2.6 Tool wear
Wear takes place at the rake and flank faces during the cutting process, regardless of the cutting parameters. Gentle or aggressive cutting parameters influence the rate tools wear and the dominance of wear mechanisms. There are five main causes of wear: 1) abrasion (mechanical wear), 2) adhesion (adhered material being sheared-off), 3) diffusive wear (diffusion between cutting tool material and workpiece material), 4) high-temperature oxidation and 5) damage to the cutting edge generated by mechanical and thermal loads (cutting edge chipping, cracks and plastic deformation). Adhesion is more likely to influence the overall wear at low temperatures, while diffusive wear and high-temperature oxidation become more relevant at high temperatures (higher cutting speed and feed rate). Abrasion occurs as contact between tool and workpiece, also defined as a two-body or counter-body wear; and eventually by other particles located between both parts also defined as a three-body wear or particle grooving [8, 47].
2.3 FINITE ELEMENT METHOD
The finite element method (FEM) or Finite element analysis (FEA) is a numerical method to solve differential equations, which is widely employed in many fields of study for finding approximate solutions to real continuous problems. It was first developed to solve problems related to structural analysis, and then it gained ground in other research fields [8]. It is commonly employed to solve problems which do not have a straightforward analytical solution.
An FE analysis can be subdivided into four main steps. The first step is the discretization of the continuum by dividing the domain into subdomains or finite elements (Figure 2-19), which requires the definition of the element form, number of nodes and interpolation function. The second step is the determination of the element equations describing the relationship between the primary unknowns such as displacement and the secondary unknowns such as stress. The third step is achieved by combining the element equations into a global matrix taking into account the boundary conditions. Finally, the last step involves solving the equation system to obtain the numerical simulation results [8].
There are several element types with 1, 2 or 3 dimensions and the user is usually free to choose them according to their necessity. The element size, at least in the testing period, should be large, in order to avoid unnecessary waste of computational resource and time [48].
