An investigation into the effects of strain rate on metals damage using continuum damage mechanics and pre-damage

نوع: Type: thesis

مقطع: Segment: PHD

عنوان: Title: An investigation into the effects of strain rate on metals damage using continuum damage mechanics and pre-damage

ارائه دهنده: Provider: Seyed Sajad Jafari

اساتید راهنما: Supervisors: Gholam Hossein Majzoobi (Ph.D)

اساتید مشاور: Advisory Professors: Ehsan Khademi (Ph.D)

اساتید ممتحن یا داور: Examining professors or referees: Golamhossein Farrahi (Ph.D), Saeid Feli (Ph.D), Amir Hossein Mahmoudi(Ph.D)

زمان و تاریخ ارائه: Time and date of presentation: 2022-02-16

مکان ارائه: Place of presentation: Online

چکیده: Abstract: Ductile damage has been the subject of many investigations over the past decades. Various models have been introduced for ductile damage with Bonora's model as one of the most well-known and applicable models. This model has proved to be accurate for quasi-static loading but loses its accuracy at high loading rates that can significantly influence the damage evolution in the material. The main objective of this study is to investigate the effect of strain rate on the ductile damage and to modify the Bonora model for taking account of the strain rate. Pure copper and copper/titanium oxide composite were selected for this investigation. In order to induce damage in the material in dynamic loading, copper samples with novel geometry were designed and manufactured. The specimens can sustain adjustable and controllable dynamic elongation without being necked or fractured. Having adjusted the elongation of the specimens, they were subjected to dynamic loading using a Split Hopkinson Tensile Bar (SHTB), by which a level of damage was introduced into the samples. After imposing a specific level of damage in the samples, they were subjected to monotonic tensile test through which the elastic modulus of the damaged specimen was obtained. Having measured the Young moduli of the damaged and undamaged specimens the damage parameter was calculated. This procedure was repeated for different strain rates and the variation of damage versus strain rate was obtained. It was shown that the results could be defined by the Bonora's model with its constants being a function of strain rate. Therefore, the Bonora damage model was modified by taking account of the effect of strain rate. The modified Bonora model was imported in Abaqus software using the user-defined field variables subroutine, VUSDFLD, for simulating the dynamic tensile loading of the specimen and studying the damage evolution in the material. The numerical results showed a reasonable agreement between the experiments, the modified Bonora model and the numerical simulations. The results revealed that damage could bring about significant strain softening in stress-strain curve of material so that, for the pure copper the ultimate strength was reduced from 225 MPa to 185 MPa. Damage evolution was also investigated for copper/titanium oxide composite. The copper powder as the matrix was reinforced by micro and macro sized titanium oxide particles. Powder metallurgy method was used to manufacture the composite samples. The powder compaction was accomplished at different rates, using the universal testing machine, Instron, for quasi-static compaction, a drop hammer for compaction at moderate loading rates and a split Hopkinson bar for high compaction rates. The compaction was conducted at different temperatures and volume fractions of 0%, 2.5%, 5%, and 10% of the reinforcing particles. The damage parameter was also calculated using the two well-known methods, density and Young's modulus methods. The results of density method showed that the increase in temperature and reduction of loading rate, the damage parameter is reduced. The results also indicated that by increasing the size and volume fraction of the reinforcing particles, the damage parameter increases. In the Young modulus method, however, tensile samples needed to be prepared. For fabricating the tensile samples the mixtures of Cu matrix and TiO2 nano and micro particles were mechanically milled, cold pressed at different loading rates (Quasi-Static, moderate and high loading rates), and finally were elongated under hot extrusion process at 850 °C. The extruded samples were then machined to prepare the standard tensile specimens for cyclic loading/unloading test. From the cyclic tests, the Young modulus was measured, the damage parameter was calculated and variation of damage parameter versus strain and strain rate was obtained. The results showed that the damage parameter increased with increase in loading rate and reinforcement volume fraction. The results also showed significant difference between the damage calculated using density and Young's modulus methods. The reason may be attributed to the fact that in density method the damage is mainly caused by the voids which come to exist during the compaction of the powder or in other words during the process of specimen manufacturing. The voids population increases with compaction rate as the trapped air between the particles have less time to exit at high loading rates. However, the fabricated samples in Young's modulus method are first extruded and then machined and finally are subjected to tensile test. Therefore, the damage in Young modulus builds up by extrusion, machining and tensile test. Again, the damage gives rise to strain-softening in stress-strain curve of material such that the ultimate strength of the Cu/TiO2 composites is reduced from 218 MPa to 179 MPa

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