Research On The Meso-statistical Analysis Method And Statistical Properties Of Metal Foams Under Tension

As a new kind of engineering materials, metallic foam possesses various excellent physical and mechanical properties including light-weight, high specific strength and stiffness, large surface, well sound insulation, high energy-absorbing capability, and novel thermal properties etc. It has been extensively used in engineering fields such as aircraft, spacecraft, automobile, and architecture and so on. In this dissertation experimental research to investigate the tensile performances of open-celled metal form was carried out , which focusing on the relation between the meso-structures and the macro mechanical performances; The meso-mechanical mechanism of deformations was analyzed; The effects of the material heterogeneous features and the structural characteristics of meso elements on the macro mechanical performances was also researched. Based on the above studies, the relationship between material property parameters and the constitutive relation is exploited. The research results and developed methods can not only realize failure mechanism of metallic foam but also do great help on meso mechanics. The details of the research include:Based on the quasi-static tensile test, the tensile mechanical performance of open-celled aluminum foams has been analyzed, and heterogeneity of the metal foam material was also studied with a focus on the impact of initial relative density upon the failure characteristics in the process of quasi-static tensile, non-uniformity of the failure in the metal foam was observed. By analyzing the experimental curves of tensile open-celled aluminum foam, this dissertation yielded a concise relation function of the open-celled foam aluminum materials under quasi-static tension.In order to investigate the heterogeneous characteristics of foam metal materials on their tensile mechanical performances, this dissertation built a one-dimension equivalent-strain grid element model to simulate metal foam, in which assuming that the elastic modulus, the yield strain, and the failure strain all meets the Weibull distribution independently. The probabilities of the elements in each tensile state were analyzed by using the statistical theory. Consequently, the multi-parameter constitutive equation of open-celled metal foam under quasi-static tension was deduced, which can rationally explain the failure curves of the tensile metal foam.By modifying Gibson-Ashby's hollow-cubic model and synthetically considering the deformations of deflection of the beam and the tension of the column, an analysis was presented for the deformation mechanism of the cubic element model, and a tensile yield strain of the hollow-cubic element model was defined, which makes the material element possessing an elastic–perfect plastic characteristic. Further by introduced the concept of plastic hinge length, the element failure model and the failure strain were determined, which let the Gibson-Ashby be used for depict the tensile of metal foam firstly.The internal heterogeneity of the metal foam was charactered by using the element structural dimension in Gibson-Ashby model as a specific statistical distribution. Further, the probability distributions of elastic modulus, yield strain and failure strain were derived. By employing the method of statistical meso-damage mechanics, the appropriate constitute relation of medium and high porosity open-celled metal foams under quasi-static tension was successfully deduced. This constitutive relation can effectively model the whole process from elasticity to material failure.Analysis is presented for the probability distribution function of medium and high porosity open-celled foam metal materials'parameters. Results showed that, only under a higher porosity do the elastic modulus, yield strain, and the failure strain of metal foam element satisfy the Weibull distribution. For metal foams of medium porosity, though the Weibull distribution did not strictly satisfy, a perfectly equivalent Weibull distribution can always be found, which firstly indicated that and these Weibull distributions are not dependent.According to the derived constitutive relation and the probability distributions of elementparameters, the probability and its variation against tensile strain of elemet in elasticity, yielding and failure were derived, The variation supports a new view, we recommended firstly, that the yield and failure state can be defined by the maximum curevatures in the stress-strain curve.? ?...