Research On Prediction Methods Of Forming Limits Under Complex Loading

The lightweight of auto-body is both opportunity and challenge for global vehiclecompany to solve problems of energy saving and environmental protection. Theapplication of lightweight materials such as high strength steel and aluminum asks forhigher standards from traditional manufacturing industry. More suitable process designand material failure criterion are urgent objectives for the current car-bodymanufacturing to include the different stress strain response from lightweight materials.The research work in this dissertation focused on the localized necking phenomenonin sheet metals of lightweight material under complex loading conditions. Three typicalproblems such as forming limits r-value dependent, path dependent and bending-radiusdependent in lightweight material applications are investigated in detail. The forminglimit prediction models under complex loading conditions are constructed to includeanisotropic effect, nonlinear strain path effect and bending effect. The physical meaningof localized necking phenomenon under complex loading is studied through thecombination of theoretical description, finite element method and experimentalapproach. The engineering approach is proposed for considering different loadingconditions to accurately predict forming limits.Main contents and innovations of this dissertation are given as follows:（1）Forming limits under complex anisotropic conditions of sheet metalsThe r-value effect on FLD under non-damage assumption is investigated in detail.The St ren-Rice’s bifurcation analysis is extended with three anisotropy coefficients aswell as the planar anisotropy in Hill’48yield criterion. Proportional loading,deformation theory of plasticity and power law relation are assumed in this planaranisotropy introduced analysis. Predicted results are also compared with experimentalobservations, and reasonable agreement is achieved. The further understanding ofr-value effect on Forming Limits from the shape changing of yield surface and plasticloading direction are constructed and discussed as main reasons for forming limitsr-value dependent phenomenon.（2）Forming limits under nonlinear strain paths with different hardening effectsThe nonlinear strain path effect on Forming Limit predictions using both isotropicand anisotropic hardening models are performed and investigated. An anisotropic hardening model based on Yoshida and Uemori development is constructed andadopted, and it is coupled with the traditional Hill’48yield surface for lightweightmaterials. The Forming Limit Diagram (FLD), Forming Limit Stress Diagram (FLSD)and Forming Limit Effective Strain Diagram (epFLD) of sheet metals subject to linearand nonlinear strain paths are analyzed and compared using the Marciniak-Kuczynskiapproach. It is found that the work-hardening behavior after the pre-straining and theloading scenario plays an important role in the path dependent behavior of forminglimits.（3）Forming limits under stretch-bending conditionThe through-thickness bending effect on the forming limits is presented forbending-radius-dependent phenomenon. The Marciniak-Kuczynski (M-K) analysis isextended to include bending effects, and models based on both flow theory anddeformation theories of plasticity are proposed. The results show that the bendingprocess decreases the sheet metal formability with the flow-theory based model, whilethe opposite is true if the deformation theory based analysis is adopted. A detailedexamination of the deformation histories from those two models reveals that theloading-unloading-reverse loading process during stretch-bending holds the key to theunderstanding of conflicting results. The “top-surface” FLD is also constructed andcompared with experimental results for the verification purpose. A hybrid approach forpredicting the forming limits after a sheet metal undergoes underContinuous-Bending-under-Tension (CBT) loading is proposed. The results show thatthe forming limits of post-die-entry material largely depends on the strain, stress andhardening distributions through the thickness direction. Furthermore, it also can be usedto evaluate the real process design of sheet metal stamping.（4）The application study of forming limits prediction in front rail for lightweightmaterialsThe theoretical FLD model under complex loading conditions is first validated withpublished Benchmark data on Numisheet2014. By focusing on the failure predictionproblem of the front rail part of auto-body in forming process, an engineering approachis then proposed for considering all complex loading effects in forming limits. Thefront rail case can be treated as a test application to solve the failure prediction problemunder the traditional forming limit. This engineering approach gives general guidelinesfor localized necking prediction in industry.