Studying The Dynamic Characteristics Of Aluminum Foams By Lagrange Analysis Method

As a new engineering material, aluminum foam has become increasingly valued by varioussectors. Due to the special microstructure of this material, it owns superior characteristicscomparing with other general materials, such as steel, aluminum, copper, etc. Aluminum foam actsas an important role in the enterprises, especial for the industries relating to impact engineering,such as the automotive industry, aerospace industry, military protection industry, etc. A lot ofresearch achievements about dynamic characteristics of aluminum foam had been done by thescholars at home and abroad. However, there exist a great of disputes in those research result, someresults were even completely contrary. Therefore, a further study of the dynamic characteristics ofaluminum foam is necessary.In view of the experimental research status of aluminum foams, in this paper, the wavepropagation method was used to study the dynamic characteristics of the aluminum foam. Thisthesis presents a modified Lagrangian analysis method called “nv+T0” Lagrange Method, whichdoes not involve the boundary stress. Starting from the path-lines method and utilizing the zero-initial condition, only from the particle velocity curve measurements the material constitutivestress-strain curves under high strain-rates can be deduced. The dynamic stress/strain wave-profilesof the PMMA material, as an example, are numerically studied by this method, which is in goodagreement with the theoretical result by using the method of characteristics, and confirms thereliability and validity of this method. This article can obtain the dynamic stress-strain curve ofaluminum foam by the “nv+T0” Lagrange method combining with the Taylor-Hopkinsonexperiment.In view of the theoretical model research status of aluminum foam, this paper introduces theRigid-Linear Hardening Plastic-Rigid Unloading （R-LHP-R） model of foam materials. therelationship between the critical position for shock disappearance Xsand the yield stress Y can bedetermined, as follow:X_s=L_oexpï¹™-Y|-（ρ_oC_pV_i）﹚=L_oexpï¹™1-Y|-σ₁﹚=L_oexp（-Y|﹙ρ_oC_p²Îµ_i）﹚（a） Among the parameters in the above equation, the specimen densityρ, the boundary stress i, theimpact velocity Vi, the undeformed length of the specimen Xs, and the original length of thespecimen L0, can be easily measured from the Taylor cylinder-Hopkinson bar impact experiments.Then the dynamic yield stress Y can be obtained from Eq.（a）. Moreover, the linear hardeningplastic modulus Epcan be determined by the measured plastic wave velocity Cp. Furthermore, thedensification strain Dcan be measured under sufficient high impact velocity. Thus all theconstitutive parameters of the R-LHP-R model can be finally determined for the tested aluminumfoam. The determined model is consistent with the Results obtained by “1sv+nv” Lagrangemethod. The strain rate sensitivity of Aluminum foam can be proved by the comparison result ofmodel and quasi-static experiment. Furthermore, the numerical simulation results of the Taylor-Hopkinson experiment verify the correctness of the results obtained by the “nv+T0” Lagrangemethod and the above model.