Overview. Local Approach to Fracture in Metal Forming: Models and Applications. Introduction

Transcription

1 12th RoundTable Simulation in Bulk Metal Forming Technology September 27th to 30th, 2010 Bamberg/Germany Local Approach to Fracture in Metal Forming: Models and Applications C. Soyarslan, A.E. Tekkaya Overview Introduction Motivation and Aim Our vision on failure analysis Failure Analysis Fracture of Materials Void Driven Failure Mechanism Fracture Strain and Triaxiality Damage Models Application Problems

2 Motivation and Aim FORMING DEFECTS Hirsch et al., 2007 Korhonen, Matinen, 2008 BULK CONVENTIONAL APPROACHES SHEET Lademo et al., 2009 Avitzur Wang 1998 Bay 2002 Uthaisangsuk et al., 2008 Analytical or experimental methods Excessive simplifications Linear Strain Paths Pure and proportional deformation modes Exclusion of hardening, anisotropy, etc No generality Expensive Poor predictive capability Uthaisangsuk et al., Motivation and Aim Analysis of microstructure development in bulk and sheet metal forming through MODELS Obtain quantitative formability limits in bulk and sheet forming Avoiding defected d products 1+1=2 Babout et al., 2003 GENERAL PHYSICAL SIMPLE Korhonen, Matinen, 2008 Stress states (low to high triaxialities) Loading rates Loading cycles Thermal conditions Physically based Experimental fit Implementation Material characterization Computational ti cost

3 Our Vision for Failure Analysis Identify and Control B747 FATIGUE SERVICE LIFE CRASH Cyclic loads Glinka, 2008 Resolve and Model DESTRUCTIVE PROCESSES Daimler AG High loading rates Impact absorbtion Safety Hambli et al., 2001 Hellström Svendsen Defense update Teng, Wierzbicki, Fracture of Materials Classification of fracture mechanisms Inclusions or secondary phases NUCLEATION GROWTH COALESCENCE Tasan,

4 Void Driven Fracture Mechanism Hydrostatic Stress Effect MVC in 1040 carbon steel Shear Stress Effect Shear microvoids in 1040 steel Fracture Strain and Triaxiality Fracture strain in triaxiality space, prediction of classical porous plasticity

5 Fracture Strain and Triaxiality Fracture strain in triaxiality space, experimental fact Fracture Strain and Triaxiality (Sheets) Characteristic stress states in sheet metal forming and the critical triaxiality interval B: Bending BB: Bending Back PS: Plane Strain BBS: Balanced Biaxial Stretching D: Drawing adapted from Valberg, Applied Metal Forming, Cambridge University Press,

6 Damage Models (General) UNCOUPLED COUPLED Fracture Criteria Micro-basedb d Damage Mechanicsh i Oyane Gurson s family Freudenthal Cockroft Latham McClintock Continuum Damage Mechanicsh i Wierzbicki - MIT FC MDM CDM Critical Plastic Work threshold Micromechanically based Abrupt failure Physical variable: VVF Uncoupled Analysis Progressive deterioration? Fully coupled Mesh independent Straightforward implementation Ease of parameter identification Shear and triaxiality dominated phases Clear interpretation of variables Strong relation to micromechanics Shear and triaxiality dominated phases Phenomenologically based Progressive deterioration Fully coupled All aspects of deterioration Sound thermodynamics Relative ease of parameter identification Shear and triaxiality dominated phases Simplistic Evaluates fracture is a [0,1] process No elastic stiffness degradation Rigorous implementation Rigorous parameter identification Mesh dependence Rigorous implementation Mesh dependence Damage Models (Fully coupled) PHENOMENOLOGICAL LEMAITRE MICROMECHANICAL GURSON Additive Lagrangian Hyperelastic Formulation Fundamental strain measure Rate Additive Corotational Hypoelastic Formulation Fundamental strain measure, Conjugate stress measure, total def. Conjugate stress measure,rate def

7 Damage Models (Yield Potentials) PHENOMENOLOGICAL MICROMECHANICAL Flow stress Equivalent stress Flow stress Equivalent stress Mean stress Damage Models (Damage Growth) PHENOMENOLOGICAL MICROMECHANICAL Void Nucleation (strain dependent) Void growth (shear enhanced) h [0,1] Growth due to Triaxiality Growth due to Shear h 0 0 h 1 h 1 No damage growth! No damage evolution for compressive principal stresses! Partial damage growth! Partial damage evolution for compressive principal stresses! Complete damage growth! No distinction between compressive or tensile principal stresses!

8 Damage Models (Void Growth-Shear) ω vs σ II /σ I for plane stress (σ III = 0). Nahshon, Hutchinson, Damage Models (Anisotropic Plasticity) PHENOMENOLOGICAL MICROMECHANICAL Quadratic-Nonquadratic Isotropic-Anisotropic Examples Meuwisse 1995, Barlat et al Hill,1948; Hill, 1990; Barlat et al., 1991, 1997,

9 3D Necking Geometry for the 3D necking problem y x z C. Soyarslan, A.E. Tekkaya, A damage coupled orthotropic finite plasticity model for sheet metal forming: CDM approach, Computational Materials Science 48 (2010) D Necking Punch load displacement curves: (a) isotropic plasticity, (b) orthotropic plasticity. (In damage coupled simulations, conventional model is utilized without unilateral damage evolution.)

10 3D Necking Equivalent plastic strain contours for damage coupled isotropic (top) orthotropic (bottom) plasticity plasticity, no unilateral damage evolution: (a) and (d) u = 2 mm, (b) and (e) u = 3 mm, (c) and (f) u = 4 mm. Introduction Failure analysis 3D Necking Application Problems Damage contours for damage coupled isotropic (top) and orthotropic (bottom) plasticity, no unilateral damage evolution: (a) and (d) u = 2 mm, (b) and (e) u = 3 mm, (c) and (f) u = 4 mm. Introduction Failure analysis Application Problems

11 Forward Extrusion C. Soyarslan, A.E. Tekkaya, Finite deformation plasticity coupled with isotropic damage: Formulation in principal axes and applications, Finite Elements in Analysis and Design 46 (2010) Forward Extrusion Soyarslan, C., Tekkaya, A.E., Akyuz, U.: Applications of Continuum Damage Mechanics in discontinuous crack formation: Forward extrusion chevron predictions, Z Angew Math Mech, 2008, 88,

12 Forward Extrusion Damage plots for, (a) 100Cr6, h=0.0, 0 (b) 100Cr6, h=1.0, (c) Cf53, h=0.0, 0 (d) Cf53, h=1.0. The maximum damage values are, (a) 5.931e-3, (b) 3.521e-1, (c) 3.770e-3, (d) 2.789e Forward Extrusion 100Cr6, contours for tensile portions of (a) max, (b) mid, (c) min principal i and (d) hydrostatic ti stresses, in MPa

13 Forward Extrusion Cf53, contours for tensile portions of (a) max, (b) mid, (c) min principal i and (d) hydrostatic ti stresses, in MPa Forward Extrusion 100Cr6, punch force-normalized process time plots for simulations with and without crack formation, and the discrete crack formation mechanism

14 Upsetting, Tension of a Notched Bar Geometry and mesh for (Left) tapered specimen, (Right) notched tensile specimen, problems. C. Soyarslan, A.E. Tekkaya, Finite deformation plasticity coupled with isotropic damage: Formulation in principal axes and applications, Finite Elements in Analysis and Design 46 (2010) Upsetting Tapered specimen, contours for tensile portions of (a) max, (b) mid, (c) min principal and (d) hydrostatic stresses, in MPa

15 Upsetting Contour plots for 65% upsetting (a) hardening variable, a, (b) damage, D Tension of a Notched Bar Damage accumulation through process history, (a) u=0.031mm, (b) u=0.063mm, (c) u=0.079mm, 079 (d) u=0.135mm. The maximum damage values are, (a) 1.906e-4, (b) 1.024e-3, (c) 1.575e-3, (d) 4.737e

16 3D Cup Drawing Geometries utilized in rectangular and circular deep drawing tests C. Soyarslan, A.E. Tekkaya, A damage coupled orthotropic finite plasticity model for sheet metal forming: CDM approach, Computational Materials Science 48 (2010) D Cup Drawing Punch Load Punch Displacement diagrams

17 3D Cup Drawing Equivalent plastic strain.contours for damage coupled isotropic (top) and orthotropic (bottom) plasticity: (Left) no unilateral damage evolution (h=1), (Right) principal stress dependent unilateral damage evolution (h=0). Introduction Failure analysis Application Problems 3D Cup Drawing Korhonen, Matinen, 2008 Damage.contours for damage coupled isotropic (top) and orthotropic (bottom) plasticity: (Left) no unilateral damage evolution (h=1), (Right) principal stress dependent unilateral damage evolution (h=0). Introduction Failure analysis Application Problems

18 Summary of Results Damage distributions for different h values h=0 h=1 h=0 h= The End Thank you for your attention and patience! Soyarslan, Celal Tekkaya, A. Erman [Celal.Soyarslan@iul.tu-dortmund.de] [Erman.Tekkaya@iul.tu-dortmund.de]