Strain rate effects on sandwich core materials an experimental and analytical investigation – homework gas quality by brand


using a modified Split Hopkinson Pressure Bar (SHPB) apparatus, consisting of polycarbon-ate bars. Foams electricity and magnetism physics definition with different density and microstructure were examined. The attainment of stress equilibrium withinthe specimen at various strain rates was examined. It was found that the stress equilibrium was reached early at lowerstrain rate as compared to higher strain rate. Both the peak stress and absorbed energy were found to be dependent onfoam density and strain rate, although foam density was found to be a more dominating static electricity sound effect factor. A model based on unitcell geometry of the closed-cell foam was also developed to predict the absorbed energy at high strain rate. Theproposed model is found to be promising in predicting the energy absorption during high strain rate loading.

Cellular foams are increasingly being used ascore materials in conjunction with high strengthskins, to produce strong, stiff and lightweight sand-wich structures for aerospace and marine appli-cations. Due to their higher impact resistance andenergy absorbing capability, cellular foams arebeing also used extensively in automobile appli-cations. The foam can be subjected to high strainrates, which are typically a couple of orders of

magnitude higher than those of quasi-static electricity in homes rates.Again, the mechanical behavior of foam dependson the structure of the cell and the density of foam.Cellular foam can be found as closed-cell or open-cell configuration. Closed-cell foams can absorbmore energy than open-cell foams because wd gaster of theentrapped gas within the cell, which acts as amedium of energy absorption. During compressionloading, the entrapped gas inside the cell can com-press either isothermally or adiabaticallydepending upon the strain rate. Thus, the mechan-ical properties of cellular foams in the context of these strain rates will be essential to the designers.Extensive studies were reported previously forboth metallic and polymeric foams at quasi-staticand lower strain rate by many authors [1–3]. High

.Traditionally the energy absorption at higherstrain rate has been calculated by using the conven-tional stress–strain relationship derived fromSHPB, which was based on the assumption that thestress equilibrium exists within the electric utility companies in california specimen dur-ing the test, and is independent of the strain rate.However, it is reported that the attainment of stressequilibrium is a function of strain rate and speci-men length [11]. Thus, the conventional stress–strain approach may not yield accurate estimationof energy absorption at high strain rate. Recently,Park and Zhou [16] have estimated the energyabsorption gas company at high strain rate using the forces andparticle velocity histories and found it to be moreaccurate. In the present study, an analytical formu-lation based on unit cell geometry for closed-cellfoam has been developed to determine the energyabsorption at various strain rates. The absorbedenergy was also calculated using both force andparticle velocity approach and the conventionalstress–strain method to assess the validity of theproposed electricity tower vector unit cell model. Time required to reachequilibrium for different strain rates was alsoinvestigated.

Conventional SHPB setup uses a long incidenceand transmitter electricity and magnetism review sheet steel bar, while a relatively shortspecimen is placed in between the bars. Schematicdiagram of the bar-specimen assembly used inSHPB setup is shown in Fig. 1. Strain gages areplaced in the incidence and transmitter bar to rec-ord strains as a function of time. The impact of thestriker bar on incidence bar results in a compress-ive incidence pulse,

eity of stress and strain fields exists within thespecimen. Estimation of energy absorption basedon non-homogenous stress–strain electricity facts ks2 relationship willnot be accurate. It is reported that the measurementof the input and output forces at two ends of thespecimen can be used as a tool to check the stresshomogeneity. The forces and particle velocities atboth ends of the specimen can be calculated asdetailed in reference [20]. Daniel and Rao [11]have shown through wave propagation analysisthat the steel–foam–steel configuration takes aboutfive times higher than polycarbonate–foam–poly-carbonate configuration to reach stress electricity allergy equilibrium.This phenomenon can be visualized through theconcept of impedance ratio,

, as explained in ref-erences [11,12]. The impedance ratio is muchlower for steel–foam–steel configuration whencompared to polycarbonate–foam–polycarbonateconfiguration. A setup with low impedance ratioyields weak transmitted wave [21–24]. Table 1shows the impedance ratio and the ratio of trans-mitted to incidence signal for both the steel–foam–steel and polycarbonate–foam–polycarbonate sys-tem. It is seen that the impedance ratio for thepolycarbonate system is almost two order magni-tude higher than the steel system, which conse-

An optical micrograph of a typical closed cellPVC foam is shown in Fig. 2a. The figure showscell edges, cell faces and their relative dimensions,as they are viewed perpendicular to cell faces. Anidealized electricity sources cubic model of the closed cell foam asshown in Fig. 2b can be extracted from thisgeometry for theoretical consideration. The cubicmodel has electricity worksheets high school cell edge thickness of

(15)Energy absorption due to isothermal com-pression of gas inside the cell occurs at two differ-ent stages similar to cell walls; elastic and plasticdeformation. The expression of energy absorptionduring elastic deformation of the cell walls can bederived after integrating the change of pressure of inside gas with respect to strain as follows [1]:[