Dislocation Density Crystal Plasticity Based Finite Element Modeling of Ultrasonic Consolidation

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Pal, D.
Stucker, B.E.

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University of Texas at Austin


A dislocation density based constitutive model has been developed and implemented into a crystal plasticity quasi-static finite element framework. This approach captures the statistical evolution of dislocation structures and grain fragmentation at the bonding interface when sufficient and necessary boundary conditions pertaining to the Ultrasonic Consolidation (UC) process are prescribed. The hardening is incorporated using statistically stored and geometrically necessary dislocation densities (SSDs and GNDs) which are dislocation analogs of isotropic and kinematic hardening respectively. Since, the macroscopic boundary conditions during UC involves cyclic sinusoidal simple shear loading along with constant normal pressure, the cross slip mechanism has been included in the evolution equation for SSDs. The inclusion of cross slip promotes slip irreversibility, dislocation storage and, hence, cyclic hardening during the UC. The GND considers strain-gradient and thus renders the model size-dependent. The model is calibrated using experimental data from published refereed literature for simple shear deformation of single crystalline pure aluminum alloy and uniaxial tension of polycrystalline Aluminum 3003-H18 alloy. The model also considers the tension-compression asymmetry in case the model is applied for deformation processes in hexagonal close packed pure Titanium and its alloy counterparts which will be investigated further in our proposed research program. One of the significant macroscopic contributions from this model development is to successfully accommodate the elasto-plastic contact problem involved in UC. The model also incorporates various local and global effects such as friction, thermal softening, acoustic softening, surface texture of the sonotrode and initial mating surfaces and presence of oxide-scale at the mating surfaces which further contribute significantly specifically to the grain substructure evolution at the interface and to the anisotropic bulk deformation away from the interface during UC in general. The model results have been predicted for Al-3003 H-18 alloy undergoing UC. A good agreement between the experimental and simulated results has been observed for the evolution of linear weld density and anisotropic global strengths macroscopically. Similarly, microscopic observations such as embrittlement due to grain substructure evolution and broken oxide layer at the UC interface has been also demonstrated by the simulation.


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