다중 상태변수를 갖는 비등방성 왜곡경화모델을 이용한 강관의 강도 이방성 예측

학위논문(박사) -- 서울대학교대학원 : 공과대학 재료공학부, 2021.8. 이명규.In this study, a numerical model for the prediction of anisotropic strengths of API steel pipe using a distortional anisotropic hardening model, namely, the HAH model, is proposed. The investigated HAH model can express the material behaviors under reverse and cross-loading paths. The multi-component evolution laws for the reverse loading behavior were additionally implemented to improve the predictive accuracy of the existing HAH model. For the stable finite element implementation of the model, the fully implicit stress update algorithm was first developed. The proposed algorithm solves a complete set of residuals as nonlinear functions of stress, equivalent plastic strain, and all the state variables of the model. Also, the consistent tangent modulus is provided. Comprehensive comparison assessments are presented regarding the accuracy and stability with different numerical algorithms, strain increments, material properties, and loading conditions. The flow stress and r-value evolutions under reverse/cross-loading conditions prove that the fully implicit algorithm with a complete set of residuals is robust and accurate, even with large strain increments. By contrast, the cutting-plane method and partially-implicit Euler backward method, which are characterized by a reduced number of residuals, result in unstable responses under abrupt loading path changes. Furthermore, as an alternative method for calculating complex first and second derivatives of the model, algorithms with analytical and numerical derivatives were studied. The developed algorithms are implemented into the finite element modeling of a large-size S-rail forming and springback. The fully implicit algorithm performs well for the whole simulation with the solely static implicit scheme. Finally, as an application of the HAH model with multi-component evolution laws, the strengths prediction of the steel plate after bending and reverse bending (BRB) deformation was conducted. The BRB test was designed to mimic the common pipe manufacturing process in a practical manner. The predicted directional strengths agree well when the HAH model is employed. By contrast, the classical isotropic hardening and iso-kinematic hardening model over- and under-estimate the strengths. The improved accuracy of the strength prediction with the investigated HAH is attributed to the anisotropic identification of the flow behavior under both load reversal and cross-loading conditions, whereas the isotropic-kinematic hardening only considers the flow behavior at load reversal.본 연구에서는 HAH 왜곡 이방경화모델을 사용하여 API 강관의 이방 강도 예측을 위한 수치 모델을 제안하였다. HAH 모델은 재료의 역 하중 또는 교차 하중 경로를 고려한 재료 거동을 표현할 수 있다. 기존 HAH 모델의 예측 정확도 향상을 위해 다성분 변화 법칙을 적용하였다. 모델을 유한요소해석에 안정적으로 적용하기 위하여 완전 내연 응력 적분법을 처음으로 제안하였다. 제안된 알고리즘은 응력, 등가 소성 변형률 및 모델의 상태변수 전부의 비선형 함수들의 잔여값을 고려하였다. 또한 다양한 적분 알고리즘, 재료 특성, 하중 조건, 변형률 증분에 따른 포괄적인 비교 평가를 수행하였다. 역/교차 하중시 모든 잔여값들을 고려한 완전 내연 알고리즘이 큰 변형률 증분에서도 강건하고 정확한 유동 응력과 r값의 변화를 예측함을 확인하였다. 반대로, 모든 잔여값들을 고려하지 않은 반-외연 또는 부분 내연 알고리즘의 경우 급격한 변형률 하중 변화에서 불안정한 해를 계산할 수 있다. 더불어, 모델의 복잡한 1차 또는 2차 미분 값의 대안을 위해 해석적인 미분과 수치적인 미분을 사용하였을 때 결과를 비교하였다. 개발된 알고리즘은 S-rail 성형 및 스프링백을 정적 내연 유한 요소법에서도 안정적으로 계산되었다. 마지막으로 다성분 변화법칙 HAH모델을 굽힘/역굽힘 이후 강판의 방향별 강도 예측에 적용하였다. 굽힘/역굽힘 실험은 일반적인 강관 생산 공정의 변형을 실질적으로 모사하기 위해 고안되었다. HAH모델 사용시 예측된 강도는 실험값과 잘 일치하였다. 하지만, 기존 등방 경화 모델이나 등방-이동 경화 모델을 사용시 강도를 정확하게 예측하지 못 하였다. 역하중에서의 거동만 고려하는 등방-이동 경화모델과 달리 역하중과 교차하중에서의 재료의 거동을 모두 고려하는 HAH모델이 더 나은 예측 정확도를 보였다.1. Introduction 1 1.1. Anisotropic strengths of the API steel pipe 1 1.2. Anisotropic hardening behaviors and models 2 1.3. Stress update algorithms 6 1.4. Predictions of the pipe strength in previous studies 8 1.5. Objectives and outlines 10 2. The homogeneous yield function based anisotropic hardening (HAH) model with multi-component evolution laws 14 2.1. Summary of the HAH hardening law 14 2.2. Evolutions of state variables for enhanced accuracy 19 2.2.1. Multi-component evolution laws for load-reversal 20 2.2.2. Latent hardening and contraction under cross-loadings 24 2.2.3. Evolutions of the microstructure deviator 25 3. Stress integration algorithms of HAH model 26 3.1. Motivation and general statement 26 3.2. Stress update algorithms for elastic-plasticity 30 3.3. Stress integration algorithms for the HAH: a review of existing algorithms 33 3.3.1. Cutting-plane method (CPM) 33 3.3.1. Euler backward method (EBM) 36 3.4. Stress integration algorithms for the HAH: proposed algorithms 39 3.4.1. Cutting-plane method (CPM) 39 3.4.2. Fully implicit Euler backward method (EBM) 41 3.5. Evaluations of stress update algorithms for the HAH 48 3.5.1. One element analysis 50 3.5.1.1. Loading condition: C5T10R 61 3.5.1.2. Loading condition: C5T10CR 68 3.5.2. Industrial problem: S-rail forming and springback 77 3.6. Summary 86 4. Anisotropic strengths prediction of steel plate after prior bending-reverse bending deformation 90 4.1. Experiments 90 4.1.1. Uniaxial tension and disk compression tests 91 4.1.2. Tension-compression-tension test and two-step tension test 95 4.1.3. Bending-reverse bending (BRB) test 97 4.2. Material modeling 100 4.2.1. Plastic anisotropy 100 4.2.2. Apparent elastic chord modulus 102 4.2.3. Monotonic stress-strain curve (without strain path change) 103 4.2.4. Anisotropic hardening behaviors under strain path changes 106 4.3. Strength prediction of the plate after bending-reverse bending 111 4.4. Discussion 121 4.4.1. Effect of hardening model 121 4.4.2. Effect of yield point phenomenon 127 4.5. Summary 135 5. Conclusion 139 Appendix A: Analytical derivatives of the HAH model 143 A.1. The first derivatives of equivalent stress 143 A.2. The second derivatives of equivalent stress 145 A.3. The first derivatives of the state variables . 147 A.4. The first derivatives of the state variables . 150 Appendix B Numerical derivatives of e-HAH model 151 Appendix C: Yld2000-2d yield function 152 Appendix D: Isotropic-kinematic hardening (IKH) model 153 Reference 155 Korean abstract 172박

Quality Assessment of Laser Welding Dual Phase Steels

Since non-conforming parts create waste for industry, generating undesirable costs, it is necessary to set up quality plans that not only guarantee product conformity but also cut the root causes of welding defects by developing the concept of quality at origin. Due to their increasing use in automotive industry, dual phase (DP) steels have been the chosen material for this study. A quality plan for welding DP steel components by laser was developed. This plan is divided into three parts: pre-welding, during and post-welding. A quality assessment regarding mechanical properties, such as hardness, microstructure and tensile strength, was also performed. It was revealed that DP steel does not present considerable weldability problems, except for the usual softening of the heat affected zone (HAZ) and the growth of martensite in the fusion zone (FZ), and the best analysis techniques to avoid failures in these steels are finite element method (FEM), visual techniques during welding procedure and digital image correlation (DIC) for post-weld analysis.The present work was done and funded under the scope of projects UIDB/00481/2020 and UIDP/00481/2020—FCT—Fundação para a Ciencia e a Tecnologia; and CENTRO-01-0145-FEDER- 022083—Centro Portugal Regional Operational Programme (Centro2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund. LAETA/INEGI/CETRIB is acknowledge due to the support provided in all research activities.info:eu-repo/semantics/publishedVersio

Review of the Synergies Between Computational Modeling and Experimental Characterization of Materials Across Length Scales

With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many applications in the development, characterization and design of complex material systems. This manuscript provides a broad and comprehensive overview of recent trends where predictive modeling capabilities are developed in conjunction with experiments and advanced characterization to gain a greater insight into structure-properties relationships and study various physical phenomena and mechanisms. The focus of this review is on the intersections of multiscale materials experiments and modeling relevant to the materials mechanics community. After a general discussion on the perspective from various communities, the article focuses on the latest experimental and theoretical opportunities. Emphasis is given to the role of experiments in multiscale models, including insights into how computations can be used as discovery tools for materials engineering, rather than to "simply" support experimental work. This is illustrated by examples from several application areas on structural materials. This manuscript ends with a discussion on some problems and open scientific questions that are being explored in order to advance this relatively new field of research.Comment: 25 pages, 11 figures, review article accepted for publication in J. Mater. Sc

RVE-size Estimation and Efficient Microstructure-based Simulation of Dual-Phase Steel

Dual-phase steel shows a pronounced structure-property correlation, caused by its internal structure consisting of asoft ferrite matrix and embedded hard martensite regions. Due to its high strength combined with high ductility, dual-phasesteel is particularly suitable for energy-absorbing and strength-relevant sheet metal applications, but its use as heavy plate isalso desirable. Due to the complex microstructure, microstructure-based simulation is essential for a realistic simulation of themechanical properties of dual-phase steel. This paper describes two important points for the microstructure-based simulation ofdual-phase steel. First a method for the straightforward experimental estimation of the RVE size based on hardness measurementsprior to tomography preparation is presented and evaluated. Secondly, a method for the efficient meshing of these microstructures,based on material definition at the integration points of a finite element model, is developed

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

On the numerical implementation of elasto-plastic constitutive equations for metal forming

National audienceThis paper is devoted to the time integration of elasto-plastic constitutive models, in view of their implementation in finite element software for the simulation of metal forming processes. Both implicit and explicit time integration schemes are reviewed and presented in algorithmic form. The incremental kinematics are also treated, so that the proposed algorithms can be used stand-alone, outside a finite element code, or they can serve to implement non-classical incremental kinematics. Full algorithms are provided, along with examples of application to non-monotonic loading for a mild steel and a dual phase steel

DAMASK: The Düsseldorf Advanced MAterial Simulation Kit for studying crystal plasticity using an FE based or a spectral numerical solver

AbstractThe solution of a continuum mechanical boundary value problem requires a constitutive response that connects deformation and stress at each material point. Such connection can be regarded as three separate hierarchical problems. At the top-most level, partitioning of the (mean) boundary values of the material point among its microstructural constituents and the associated homogenization of their response is required, provided there is more than one constituent present. Second, based on an elastoplastic decomposition of (finite strain) deformation, these responses follow from explicit or implicit time integration of the plastic deformation rate per constituent. Third, to establish the latter, a state variable-based constitutive law needs to be interrogated and its state updated.The Düsseldorf Advanced MAterial Simulation Kit (DAMASK) reflects this hierarchy as it is built in a strictly modular way. This modular structure makes it easy to add additional constitutive models as well as homogenization schemes. Moreover it interfaces with a number of FE solvers as well as a spectral solver using an FFT.We demonstrate the versatility of such a modular framework by considering three scenarios: Selective refinement of the constitutive material description within a single geometry, component-scale forming simulations comparing di_erent homogenization schemes, and comparison of representative volume element simulations based on the FEM and the spectral solver