NSM LAB Net Shape Manufacturing Laboratory Development of oil canning index model for sheet metal forming products with large curvature Speaker: M.S. Eng. Mohanraj Murugesan Ph.D. Candidate/Researcher – Sogang University (South Korea) 정형가공연구실

Presentation Outline What’s oil-canning Motivation and overall objective Material properties estimation Stamping process and indentation test results Proposed oil canning index model Model validation and verification Summary On-going research work

Test procedure to estimate minimum load to cause oil-canning. What's oil-canning Oil canning is a moderate deformation or an elastic buckling problem of sheet material & usually occurs at unsupported area of a body panel when a load is applied to the area.  This terminology also refers to the popping sound made when pressure is applied to the deformed sheet forcing the deformation in the opposite direction. Reasons: Effect is extremely large when panel thickness is very small & panel width is too large. Effect is increased when sheet metal has large curvature & low panel stiffness. (stamping/deep drawing) Caused by unequal stretching of the material. Typically caused by uneven stresses at the fastening points. Test procedure to estimate minimum load to cause oil-canning.

Motivation Automobile Parts Roof Panels Home Appliances Aircraft Components

Overall Objective Oil-canning experiment Identification of main factors Develop oil-canning prediction model Sensitivity analysis Modify material properties Oil-canning prediction model Model validation Model verification Automobile parts Home Appliances Applications Aircraft Components Roof Panels

Material Properties Estimation A measure of planar anisotropy A measure of normal anisotropy 𝑅 = 𝑅 0 +2 𝑅 45 + 𝑅 90 4 R0, R45 and R90 represents anisotropy values at directions, 0°, 45° and 90°, respectively. Fig 1. Tensile test set-up Fig 2. Stress-strain curve from tensile test ε 𝑤 : strain at width direction ε 𝑡 :strain at thickness direction ε 𝑙 : strain at length direction R=− ɛ 𝑤 ɛ 𝑡 + ɛ 𝑙 Lankford variable Material R0 R45 R90 ΔR 𝑹 EGI steel 3.0414 1.8586 3.3977 1.3609 2.5391 GI steel 2.3767 2.7833 3.4373 0.1237 2.8451 Table 1. Material anisotropy values.

Stamping Process Initial plate size : 280 x 375 mm 2 Blank holding force : 250 N Plate thickness : 0.6, 0.7, 0.8 Friction co-efficient : 0.1 Materials used : GI steel and EGI steel Punch velocity : 13 m/s Embossing depth : 4mm Bead length : (a) 0mm (b) 7.854mm (c) 9.3858mm Fig 3. Stamping process experiment setup. Fig 4. Stamping process FE model.

3D scanning procedure Purpose: To measure the curvature of plate Measurement of thickness distribution using the formed part Verification with numerical model (Curvature and thickness distribution comparison) Curvature Specimen 3D scanning camera Fig 6. 3D Scanning Procedure Fig 5. 3D scanning set-up with stamped part Fig 7. Stamped part for scanning

Horizontal curvature ( 𝑚 −1 ) 9 Curvature measurements from 3D Scanning P1 P2 P3 0.6mm(EGI Steel) case Vertical bead force Horizontal bead force Horizontal curvature ( 𝑚 −1 ) Vertical curvature ( 𝑚 −1 ) Horizontal curvature 1 No bead 0.121 0.105 1.14 0.189 0.145 0.348 2 Low 0.173 0.122 0.217 0.069 0.17 0.77 3 High 0.408 0.788 2.82 0.055 0.316 0.682 4 0.388 0.902 3.68 0.44 5 0.79 0.09 0.109 0.065 6 0.039 0.832 0.175 0.05 7 0.06 0.089 0.764 0.235 0.072 0.076 8 0.054 0.939 0.161 0.056 0.015 9 0.058 1.06 0.176 0.014 P2 P3 P1 Horizontal Vertical 0.7mm(GI Steel) case Vertical bead force Horizontal bead force Horizontal curvature ( 𝑚 −1 ) Vertical curvature 1 No bead 0.842 1.06 1.39 0.084 0.853 1.08 2 Low 0.019 0.441 0.278 0.013 3 High 0.647 0.796 1.38 0.53 0.804 4 0.576 1.79 0.608 0.955 5 0.053 0.592 0.07 0.045 6 0.02 1.13 0.153 7 0.081 0.437 0.33 8 0.269 0.133 1.55 0.083 0.293 0.285 9 0.098 1.04 * Curvature value = 0  this means the specimen is flat and there is no curvature

Curvature measurements from 3D Scanning 10 Curvature measurements from 3D Scanning P1 P2 P3 0.8mm(EGI Steel) case Vertical bead force Horizontal bead force Horizontal curvature ( 𝑚 −1 ) Vertical curvature 1 No bead 0.15 0.221 1.45 0.19 0.036 0.053 2 Low 0.052 0.038 0.888 0.232 0.051 0.04 3 High 0.241 0.247 1.95 0.23 0.25 4 0.451 0.466 1.36 0.348 0.422 5 0.071 0.9 0.203 0.081 6 0.011 0.666 0.158 0.033 7 0.084 0.805 0.17 0.028 8 0.019 1.16 9 0.022 1.09 0.212 P2 P3 P1 Horizontal Vertical * Curvature value = 0  this means the specimen is flat and there is no curvature

Indentation test procedure Purpose: To determine whether oil canning phenomenon occurs or not  in the stamped part. Obtain load-displacement curve.  Choose three points where the curvature is most likely to occur in the stamped part. Punch Stamped part Specimen holder Fig 8. Indentation test using stamped part Fig 11. Load-stroke curve for 0.7mm GI steel Fig 10. Load-stroke curve for 0.7mm GI steel Fig 9. Finite element model for numerical simulation

Indentation test results 12 Indentation test results Purpose: To determine whether oil canning exists for the particular test location and what is the minimum load to cause oil canning. Bead force in vertical location high and no bead force in horizontal location. Bead force in horizontal location low and no bead force in vertical location. Oil canning at locations P1 and P3. Bead force in vertical location low and no bead force in horizontal location. Oil canning at location P2. P2 P3 P1 Horizontal Vertical 0.6mm (EGI Steel)

Indentation test results 13 Indentation test results Bead force in vertical location high and no bead force in horizontal location. Bead force in horizontal location low and no bead force in vertical location. Oil canning at locations P1 and P3. Oil canning at location P2. No bead force in horizontal and vertical location. P2 P3 P1 Horizontal 0.7mm (GI Steel) Vertical

Indentation test results 14 Indentation test results Bead force in vertical location high and no bead force in horizontal location. Bead force in horizontal location low and no bead force in vertical location. Oil canning at locations P1 and P3. Low bead force in both horizontal and vertical location. P2 P3 P1 Horizontal 0.8mm (EGI Steel) Vertical

Indentation test results According to thickness (t), curvature (R) and residual stress ( 𝜎 1 , 𝜎 2 ) : In the absence of initial stress, the smaller radius, R, (the greater curvature), the possibility of no oil-canning. In the absence of initial stress, as the thickness increases, the buckling load also increases. The possibility of oil-canning is decreasing. 0.6mm (EGI Steel) 0.7mm (GI Steel) Fig 12. Load-displacement curve from indentation test for GI and EGI steel

Indentation test results If the R value is less than 1000, the oil canning effect is reduces and vice versa. Here the thickness is kept constant as 0.6mm for all the experiments. 0.6mm (EGI Steel) R = 6000 mm R = 1000 mm R = 600 mm

Fig 13. Radius of curvature estimation Proposed Oil Canning Index Model For oil canning damage value estimation, the empirical model can be expressed as follows: A00 to A20 are the material constants. t*, σ* represents the geometric parameters and the residual stresses, respectively. Based on the geometric factors, we propose a mathematical model for the risk of oil canning effect as follows: 𝑓( 𝑡 ∗ , 𝜎 ∗ )= 𝐴 00 + 𝐴 10 𝑡 ∗ + 𝐴 01 × 𝜎 ∗ + 𝐴 20 (𝑡 ∗ ) 2 + 𝐴 11 𝑡 ∗ 𝜎 ∗ + 𝐴 02 𝜎 ∗ 2 R : Radius of curvature w: Panel width T : thickness ν : Poisson’s ratio k : width to length ratio E : Young’s modulus If OC ≥ 1, Oil Canning If OC < 1, No Oil Canning Fig 13. Radius of curvature estimation

Proposed Oil Canning Index Model “OCPF (Oil Canning Prediction Factor)” model “OCDV (Oil Canning Damage Value)” model 𝑓( 𝑡 ∗ , 𝜎 ∗ )= 𝐴 00 + 𝐴 10 𝑡 ∗ + 𝐴 01 × 𝜎 ∗ + 𝐴 20 (𝑡 ∗ ) 2 + 𝐴 11 𝑡 ∗ 𝜎 ∗ + 𝐴 02 𝜎 ∗ 2 𝑡 ∗ = thickness radius × length width 𝜎 ∗ = 𝜎 1 + 𝜎 2 + 𝜎 1 𝜎 2 𝒇 𝒕 ∗ , 𝝈 ∗ =𝟏𝟗.𝟗−𝟕𝟑.𝟒 𝒕 ∗ +𝟐.𝟏𝟗 𝝈 ∗ +𝟏𝟖𝟖 (𝒕 ∗ ) 𝟐 −𝟐.𝟗𝟒 𝒕 ∗ 𝝈 ∗ +𝟎.𝟗𝟐 𝝈 ∗ 𝟐 𝜎 ∗ 𝑡 ∗ Fig 14. Oil Canning Prediction Factor Fig 15. Proposed Oil Canning Model using Experimental Data

Model verification using experimental results Pexperiment : Buckling load from experiment Pprediciton : Buckling load from prediction 𝒇 𝒕 ∗ , 𝝈 ∗ =𝟏𝟗.𝟗−𝟕𝟑.𝟒 𝒕 ∗ +𝟐.𝟏𝟗 𝝈 ∗ +𝟏𝟖𝟖 (𝒕 ∗ ) 𝟐 −𝟐.𝟗𝟒 𝒕 ∗ 𝝈 ∗ +𝟎.𝟗𝟐 𝝈 ∗ 𝟐 t case point curvature width length 𝝈 𝟏 𝝈 𝟐 Pexperiment Pprediction Error (%)

Summary Anisotropic material properties was estimated from simple tensile test experiments. Stamping experiment was conducted and then curvature radius was measured from 3D scanning procedure. Further the load-displacement curve was obtained from the indentation test. From the load-stroke curve, the minimum load to cause the oil canning was estimated. Surrogate modeling method was utilized to develop the oil-canning prediction model for future predictions. Later the model verifications were done using enormous experimental data. Overall proposed oil-canning model showed quite good agreement with the experimental data. We found that the panel thickness, the curvature radius and the residual stresses plays major role.

Challenging Tasks and Future Work Further empirical model implementation is required. The identification of main factors are quite sensitive. So we are planning to do more experiments using the real specimens such as home appliances or automobile parts or aircraft components or roof panels. As well as we decided to develop a oil canning prediction model for each applications separately.

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