Stress Analysis of a Rocket Engine Copper Alloy Using Gurson Micromechanical Model

Failure of structures due to overloading can be classified into two types brittle and ductile failures. The former occurs in materials having limited plastic deformation capability (brittle materials) whereas the latter is observed in ductile materials. The vast field of linear elastic fracture mechanics is available to study brittle failures whereas for ductile failures, one has to resort to damage mechanics based theories. In this research work, the Gurson-Tvergaard-Needleman micromechanical model available in the ANSYS (Version 15.0) general purpose finite element analysis software code is utilized for failure analysis of a high thermal conductivity-high ductility copper alloy. It is used as the inner wall material in a double walled cryogenic rocket engine thrust chamber in which the outer wall is made of stainless steel. The thrust chamber experiences hot and cold (cryogenic) temperatures during its operation. It is required to find out the ultimate load carrying capability of this special copper alloy by the Gurson micromechanical model at different temperatures including room temperature, elevated and cryogenic temperatures. Published tensile test results for the above material at 550K, 300K, 77K and 20K are used for the constitutive modeling of the material. The well-known Multilinear Isotropic Hardening model in combination with the GTN model is used for simulation of the material behavior. The GTN parameters of a material consist of 9 constants which have to be calibrated by comparing engineering stress strain graphs of a tensile test specimen with those from finite element analysis. This has to be done by a trial and error procedure till the constants used results in a good match between the engineering stress strain graphs. Both geometric and material nonlinear analysis features are used for this. One of the merits of GTN model is that it can account for the effect of hydrostatic stress on the failure of a material. Therefore, the GTN model has been used for the study of growth of ductile cracks in a material. The generation and evolution of a macro crack in the tensile specimen at room temperature has been attempted using the GTN model parameters evaluated by the above method. The Element Birth and Death feature available in ANSYS has been employed to simulate the above effect.