27.5 Discussion It has been shown that the use of numerical models to accurately represent a structure subjected to impact loads is certainly within the capability of current software codes. Numerical codes provide designers with a high level of flexibility, allowing them to explore many different aspects of an impact event without the need for expensive experimental set ups. During this study the results between simulation and experiment were in good agreement, although a few differences were noticed. It is important that the selected material model can accurately capture the behavior of the materials in the structure and that the geometries and loads depicted by the model are as close as possible to the actual experiment. In some cases, high sensitivity to small geometric differences was noted. Many different numerical representations are available for adhesive materials including cohesive elements and different tie-break options. The implementations investigated provided accurate prediction for structural performance at the macro level. By this, it should be understood that the load–displacement diagram generated by the model and the predicted deformations were in good agreement with the actual structure under the same loading conditions as in the actual experiment. The numerical implementations investigated did not consider strain rate effects. While this is not important for quasistatic events, strain rate effects can be important for dynamic conditions. Although the model did not account for strain rates in the adhesive material, strain rates generated in the dynamic test were low enough that it made no significant difference between the experiments and the simulations. At higher velocities, or for different joint designs, strain rates could have a more significant impact. As was previously shown, the mechanical properties of this particular adhesive are sensitive to strain rate, which suggests that models must include provisions for strain rate effects. To obtain a better insight into joint stresses, crack propagation and bond failure, a more complex model is required, ideally a series of solid elements with the proper material model. At this level of detail, the material description will require properties that are join dependent, such as the appropriate traction separation curve, besides the intrinsic properties of the material itself such as yield stress and energy release rate in the required range of expected strain rates. In global terms, either cohesive elements or tie-breaks can accurately predict crush tube structure responses, and capture the behavior of the adhesive joint, but cannot provide a more detailed description of the failure process inside the material. Material damage mechanisms such as crazing and shear bands which are typical of epoxy materials during loading need to be characterized and understood before more detailed modeling can be implemented. Unfortunately, models assembled in the manner described in this work do not produce any insights regarding the damage mechanism that triggers ultimate failure. At this point, further research is required to characterize damage in epoxy materials and to understand how these failure modes would be affected by changes in dynamic load rates and by the interaction of different materials in the joint. Acknowledgement The authors gratefully acknowledge the use of SHARCNET computing facilities, material testing undertaken by Jeff Wemp and Christopher Thom, and support from the Ontario Centre’s of Excellence (OCE) and 3M Company. References 1. Cui X, Zhang H, Wang S, Zhang L, Ko J (2011) Design of lightweight multi-material automotive bodies using new material performance indices of thin-walled beams for the material selection with crashworthiness consideration. Mater Des 32:815–821 2. Shariatpanahi M, Masoumi A, Ataei A (2008) Optimum design of partially tapered rectangular thin-walled tubes in axial crushing. Proc Inst Mech Eng Part B J Eng Manuf 222:285–291 3. Peroni L, Avalle M (2006) Experimental investigation of the energy absorption capability of bonded crash boxes. Trans Built Environ 87:445–454 4. Avalle M, Peroni L, Peroni M, Scattina A (2010) Bi-material joining for car body structures: experimental and numerical analysis. J Adhes 86:539–560 Table 27.3 Summary dynamic impact for structures bonded with DP-460NS; simulation versus experiment results Measurement Hats Exp Coh TB1 TB2 Energy absorb [kJ] 1.480 1.450 1.460 1.460 Specific energy abs [kJ/kg] 3.370 3.300 3.320 3.320 Mean force [kN] 33.10 37.96 39.92 36.54 Peak force [kN] 136.2 159.8 156.6 160.1 27 Adhesively Joined Crush Tube Structures Subjected to Impact Loading 223
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