A Study For Ductile Fracture Under High Strain Rate And Low Stress Triaxiality Tension Based On Void Coalescence

In this doctoral dissertation, typical ductile metal-pure copper is the main reseach object.This dissertation mainly studies ductile tension fraction and related constitutive equationunder high strain rate and low stress triaxiality. The following are the innovations in thisdissertation:1) Thermoviscoplastic constitutive equations of typical ductile material-a pure copperwere determined and adjusted with considering the third deviatoric stress invariant (Lodeangle parameter) dependence [Bai et al. Int. J. plasticity24,1071(2008)] to describe largerstrain of the pure copper bars and sheets:In order to analyse and predict the effect of high strain rate and low stress triaxialityon tension fracture of bars and sheets made of typical ductile material-a pure copper, welldefined thermoviscoplastic constitutive equations of the pure copper were determined fromthe first tension loading in the optimized tensile split Hopkinson bar (TSHB) tests for copperbars and sheets, considering the third deviatoric stress invariant (Lode angle parameter)dependence. In order to describe large strain of pure copper bars and sheets, the determinedthermoviscoplastic constitutive equations were adjusted in numerically simulating the largedeformations including the diffuse necking of pure copper bars and sheets generated by themulti-tension loading in TSHB tests and recorded by a high speed camera.2) The dynamic diffuse necking of pure copper bars was investigated with verifyingBatra criterion [Int. J. Impact Eng.34,448(2007)] for thermoviscoplastic instability:It was found that the surface wrinkles on pure copper bars recorded by the high speedcamera in TSHB tests were connected to the diffuse necking which are more complexphenomena than in static case due to inertia, thermal softening and strain rate hardening andneed well understanding. The instability criterion for homogeneous simple tensiledeformations of a thermoviscoplastic bar presented recently by Batra et al with perturbationmethod was verified by the comparison between the recorded strain at which the surfacewrinkles on pure copper bars occur and the estimated strains according to Batra criterion andour adjusted theomoviscoplastic constitutive equation for pure copper bars.3) A novel fracture testing under high strain rate and low stress triaxiality tension wasdeveloped to interrupt the test at different levels of deformation:It was realized to interrupt, isolate and identify the various stages of the dynamicfracture process of pure copper bars under impact tension, by using our designed high-speed tensile facility (HSTF) tests in which multiple-bars with special fixture were tested andcontrolled at different levels of elongation in a single test. It was shown that diffuse neckingof bars developed into localized necking, and voids within the necking zone nucleated, grewand coalesced as the controlled elongation increased. Different mechanisms of voidcoalescence in pure copper were observed from scanning electron microscopical (SEM)investigation: stable coalescence through impingement of primary voids; unstable coalescencethrough necking and shearing of the primary intrevoid ligament.4) A numerical simulation method was presented with involving dynamic evolution ofa characteristic void:A numerical simulation method with a characteristic void identified by Ragab[Eng.Fract. Mech.71,1515(2004)] experimentally was presented by using our adjustedthermoviscoplastic constitutive equation for pure copper bar to analyse and predict the effectsof strain rate and stress triaxiality on tension deformation and fracture of pure copper bars inTSHB tests and interrupted HSTF tests. The variations of stress triaxiality and strain rate withtime in necking zone computed with the numerical simulation method were connected to theSEM investigation for recovered localized necking zones. It was found that although thestress triaxiality is a maximum in the middle of the necking zone, void evolution at a positionnear the surface of minimum cross-section of the necking zone was more severe than in themiddle of the necking zone, which may be connected with the finding discussed by Alves[J.Mech. Phys. Solids47,643(1999)]“a crack started to run probably from the notch root,certainly not from the middle where the triaxiality is a maximum.”5) A dynamic void instability criterion was presented based on void shape evolution:A dynamically computational void cell model was presented for pure copper toanalyse and predicted the localized fracture strains and the critical impact velocity in tensionof pure copper bars. The instability criteria obtained from quasi static numerical simulation[Pardoen et al., J. Mech. Phys. Solids48,2467(2000). Benzerga, J. Mech. Phys. Solids50,1331(2002)]were discussed and a dynamic void instability criterion based on void shapeevolution was presented, which predicted the fracture strains consistent with the experimentalresults of pure copper bars in TSHB tests and the critical impact velocity of pure copper intension consistent with the experiments in HSTF tests.6) A method for investigating the dynamic coalescence mechanism of void cluster wasdeveloped with proposing a dynamic criterion for void coalescence:In order to visualize void growth and coalescence in a controlled matter, the dynamicgrowth, coalescence and evolution post coalescence of drilled simplest cluster voids in purecopper sheets subjected to the multi-tension loading in the TSHB tests were recorded by the high speed camera and simulated by using our adjusted constitutive equation of the purecopper and the different criteria for void coalescence. This study presented a stress triaxialityand strain rate (STSR) dependent failure criterion for void coalescence to reveal the voidcoalescence process. The experimentally recorded void evolution at a certain average strain ofpure copper sheets were compared with the numerically simulated results, which involved theSTSR dependent failure criterion, the localized Thomason criterion[Ductile fracture of metals(Pergamon Press,1990), Fatigue Frac Eng Matter Struc.21,1105(1998)] and Brown-Embury criterion[Proceeding of3rd international conference on strength of metals and alloys1973. p.164~173.]. The validity of void coalescence criteria was assessed: the STSRdependent failure criterion could be used to describe the void coalescence process while thelocalized Thomason criterion and Brown-Embury criterion for void cluster could also matchthe process of void coalescence to a certain extent.