Investigation of Single Point Incremental Sheet Forming Process: Extraction of Constitutive Models and Parameters Optimization

다국어 초록 (Multilingual Abstract)

The incremental forming process (ISF) is one of the prominent sheet metal manufacturing techniques among the traditional forming methods; it’s becoming more noticeable these days due to its flexibility for manufacturing complex parts without utilizing predefined forming dies. Besides, the ISF process has higher formability of formed parts at a low cost than the conventional sheet forming methods. Additionally, the consistent and reasonable work material characterization in both room and warm temperature conditions under various strain rates is remarkably essential for modeling the numerical simulation and optimizing the sheet metal forming process working parameters. This research work’s contributions to the ISF process can be organized into the following sections: at first, the field emission scanning electron microscopy (FESEM) analysis combined with the energy-dispersive X-ray spectroscopy (EDS) technique is employed to conduct the elemental identification investigation. Secondly, the Digital Image Correlation (DIC) technique is used to investigate the work materials for assessing their material properties. For this purpose, the digital images at each deformation step, which provide complete displacement and strain data information until the fracture more accurately, are used. Further, the empirical models such as the original and modified Johnson-Cook models, modified Zerilli-Armstrong model, the strain-compensated Arrhenius-type constitutive equation, and hybrid machine learning model are proposed for describing the material flow behavior during hot deformation conditions. Overall, the proposed constitutive equation from the artificial neural network model combined with an optimization approach is proved to have good predictability in flow stress estimation. Eventually, the single incremental forming process (SPIF) is modeled using a customized vertical milling machine to investigate the SPIF process. The design of experiments (DOE) combined with the grey relational analysis (GRA), the response surface methodology (RSM), and statistical analysis of variance (ANOVA) is adopted for determining the process parameter's influence on the material formability without producing a rupture. The DOE procedure, a face-centered central composite design, is adopted for the AA3003-H18 Al alloy sheets for conducting the tests. The RSM procedure is used for optimizing the process parameters and identify the optimal experimental conditions. The statistically proposed model is observed from the outcome to be in good agreement with the experimental measurements. ANOVA is conducted to explain the proposed model's adequacy and the input factor's influence on the output factor. The statistically proposed regression model is observed to agree with the experimental estimations, having a higher R2 (0.8931) with lower prediction error (2.78%). The process parameters, such as step size, feed rate, the interaction effect of tool radius and step size, positively influence the response variable. Similarly, the input factors are optimized using the Taguchi method to minimize the surface roughness of formed parts. Firstly, according to the smaller-the-better, the S/N ratios are estimated to make a response table for getting the optimum level of process parameters. Minimum surface roughness is accomplished when the vertical step-size is smaller, the feed-rate is high, and the forming tool radius is high. The optimum level setting is acquired at 3.0 mm of forming tool radius (level 3), 3000 rpm of spindle speed (level 1), 0.10 mm of vertical step size (level 1), and 2000 mm/min of feed rate (level 4). The ANOVA results such as p-test and F--test revealed that vertical step-size, feed-rate, and tool radius significantly affect surface roughness. In contrast, the spindle speed is witnessed to have no significant influence on surface roughness. The Taguchi design results conferred better agreement with the actual measurements with moderate model error (approximately 1.8%). Additionally, the microstructural evaluation revealed that the thinning behavior tended to increase as forming depth reached its maximum; the material deformation was also observed to be uniform and homogeneous.

국문 초록 (Abstract)

ISF(점진 성형 공정)는 기존의 성형 방법 중 대표적인 판금 제조 기법 중 하나다. 사전 정의된 성형 다이를 활용하지 않고 복잡한 부품을 제조할 수 있는 유연성으로 인해 오늘날 더욱 주목을 받고 있다. 게다가, ISF 공정은 기존의 시트 성형 방법보다 저렴한 비용으로 성형 부품의 성형성이 우수하다. 또한 다양한 변형률 하에서 실내 및 온열 온도 조건 모두에서 일관되고 합리적인 작업 재료 특성은 수치 시뮬레이션을 모델링하고 판금 성형 공정 작업 매개 변수를 최적화하는 데 매우 중요하다. 본 연구의 ISF 공정에 대한 기여는 처음에는 field emission scanning electron microscopy (FESEM) 분석과 에너지 분산 X선 스펙트럼 분석(EDS) 기법을 결합하여 소자 식별 조사를 실시하는 섹션으로 나눌 수 있다. 둘째, DIC (Digital Image Correlation) 기법을 사용하여 재료 특성을 평가하기 위한 작업 재료를 조사한다. 이를 위해 파단까지의 변위 및 변형 데이터 정보를 제공하는 각 변형 단계의 디지털 영상이 사용된다. 또한, 고온 변형 조건에서의 재료 흐름 거동을 설명하기 위해 최초 및 수정된 Johnson-Cook 모델, 수정된 Zerilli-Armstrong 모델, 변형률 보정 Arrhenius형 구성 방정식, 하이브리드 기계 학습 모델 등의 경험적 모델을 제안한다. 전반적으로, 인공신경망 모델의 제안 구성 방정식은 최적화 접근법과 결합된 흐름 응력 추정에 좋은 예측 가능성을 가지고 있는 것으로 입증되었다. 결국, 단일 점진 성형 공정(SPIF)은 SPIF 공정을 조사하기 위해 맞춤형 수직 밀링 머신을 사용하여 고안되었다. Grey relational analysis (GRA), response surface methodology (RSM), statistical analysis of variance (ANOVA)과 결합된 실험 설계(DOE)는 공정 매개변수가 파열을 일으키지 않는 상황에서 재료 성형성에 미치는 영향을 위해 채택되었다. 실험 실행을 위한 AA3003-H18 Al 합금 시트에 표면 중심의 중앙 합성 설계인 DOE 절차가 채택되었다. RSM 절차는 공정 변수를 최적화하고 최적의 실험 조건을 식별하는 데 사용된다. 통계적으로 제안된 모델은 실험 측정과 잘 일치하는 결과로부터 관찰된다. ANOVA 분석은 제안된 모형의 적합성과 입력 인자가 출력 인자에 미치는 영향을 설명하기 위해 수행된다. 통계적으로 제안된 회귀 모형은 더 높은 결정 계수(R2)(0.8931)와 더 낮은 예측 오차(2.78%)를 갖는 실험 추정과 일치하는 것으로 관찰된다. 스텝 크기, 이송 속도, 공구 반지름의 상호작용 효과, 스텝 크기와 같은 프로세스 파라미터는 반응 변수에 긍정적인 영향을 미친다. 마찬가지로 입력 계수는 Taguchi 방법을 사용하여 최적화되어 성형 부품의 표면 거칠기를 최소화한다. 첫째, 작을수록, S/N 비율은 프로세스 매개변수의 최적 수준을 얻기 위한 반응 표를 만드는 것으로 추정된다. 최소 표면 거칠기는 수직 스텝 크기가 작고 이송 속도가 높으며 성형 공구 반경이 높을 때 이루어진다. 최적의 레벨 설정은 성형 공구 반경 3.0mm (레벨 3), 스핀들 속도 3000rpm (레벨 1), 수직 스텝 크기 0.10mm (레벨 1), 이송 속도 2000mm/min (레벨 4)에서 획득한다. P-시험 및 F-시험 등의 분산 분석 결과에 따르면 수직 단계 크기, 공급 속도 및 공구 반경은 표면 거칠기에 상당한 영향을 미친다. 반면, 스핀들 속도는 표면 거칠기에 큰 영향을 미치지 않는 것으로 확인되었다. Taguchi 설계 결과는 중간 정도의 모형 오차(1.8%)를 갖는 실제 측정값과 더 잘 일치하는 결과를 얻었다. 또한 미세구조 평가 결과 형성 깊이가 최대에 도달하면 박리 거동이 증가하는 경향이 있었으며 재료 변형도 균일하고 균일한 것으로 관찰되었다.

목차 (Table of Contents)

• 1 Single Point Incremental Forming Process 1
• 1.1 Background 1
• 1.1.1 Cold Incremental Forming Process 1
• 1.1.2 Hot Incremental Forming Process 6
• 1.2 Organization of the Dissertation 8
• 1.3 Toolpath Strategies 9
• 1.4 Surface Quality 12
• 1.5 Applications 13
• 1.6 Effects of Process Parameters 14
• 1.7 Process Modeling and Simulation 15
• 1.8 Selection of Lubrication 16
• 1.9 Material Characterization 21
• 1.9.1 Material Test 21
• 1.9.2 Uniaxial Tensile Test 22
• 1.9.3 Measurements of Strain-hardening Models 25
• 1.9.4 Plastic Anisotropy 26
• 1.9.5 Hot Tensile Test of AISI-1045 Steel 29
• 1.9.6 Microstructural Characterization 31
• 1.10 Conclusions 34
• 2 Johnson-Cook Material and Failure Models 35
• 2.1 Summary 35
• 2.2 Introduction 36
• 2.3 Johnson-Cook Material Model 38
• 2.3.1 Determination of Material Constants B and n 39
• 2.3.2 Determination of Material Constant C 40
• 2.3.3 Determination of the Material Constant, m 41
• 2.4 Johnson-Cook Damage Model 44
• 2.5 Discussion 48
• 2.6 Conclusions 53
• 3 Modified Johnson-Cook and Zerilli-Armstrong Models 55
• 3.1 Summary 55
• 3.2 Introduction 56
• 3.3 Modified Johnson-Cook model 58
• 3.3.1 Determination of constants A1, B1, B2 58
• 3.3.2 Determination of constant C1 59
• 3.3.3 Determination of constants λ1, λ2 60
• 3.4 Modified Zerilli-Armstrong Model 61
• 3.4.1 Determination of constants C2 and n 63
• 3.4.2 Determination of constants C3 and C4 64
• 3.4.3 Determination of constants C5 and C6 66
• 3.5 Discussion 68
• 3.6 Conclusions 74
• 4 Arrhenius-Type Constitutive and Artificial Neural Network Models 77
• 4.1 Summary 77
• 4.2 Introduction 78
• 4.3 Strain Compensated Constitutive Equation 81
• 4.3.1 Arrhenius-Type Constitutive Equation 81
• 4.3.2 Strain Compensation 84
• 4.3.3 Constitutive Model Verification 85
• 4.4 Artificial Neural Network Model 87
• 4.4.1 Proposing Flow Stress Model using ANN-BP Algorithm 87
• 4.4.2 Optimization Procedures for Obtaining the Best ANN-BP Model 90
• 4.5 Conclusions 95
• 5 SPIF Process Optimization using Response Surface Methodology 99
• 5.1 Summary 99
• 5.2 Introduction 100
• 5.3 Experimental Procedures 101
• 5.4 Design of Experiments 103
• 5.5 Grey Relational Analysis 105
• 5.6 Response Surface Methodology 110
• 5.7 Results and Discussion 112
• 5.8 Conclusions 122
• 6 Taguchi Method in Optimization of Surface Roughness 125
• 6.1 Summary 125
• 6.2 Introduction 126
• 6.3 Experimental Design using Taguchi method 127
• 6.4 Microstructure Evaluation of AA5052-H32 material in SPIF Process . 132
• 6.5 Microstructure Evaluation of AA3003-H18 material in SPIF Process . 135
• 6.6 Conclusions 137
• 7 Conclusions and Future Work 139
• 7.1 Conclusions 139
• 7.2 Suggestions for the Future Work 142
• Bibliography 145

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