Overview
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The Structures and Materials Group addresses three key areas. Structural Analysis selects from existing large-scale codes, modeling software, and post-processing software to establish the best starting points to develop center-wide capabilities for full-scale stress analysis for the whole rocket. Solid-Combustion-Fluid Interface develops the strategy, theory, and key numerical algorithms needed to interface the finite element code developed through Structural Analysis with the combustion and fluid mechanics parts of the whole-rocket simulations. Failure Analysis initiates development and implementation of modeling schemes to perform detailed investigation of failure processes in the various rocket materials, e.g., metals, composites (fiber reinforced polymeric and metal matrix composites) and solid propellant.
This group focuses on the concurrent execution of stress/deformation analyses for structural performance and integrity using an integrated suite of multiscale, multiphysics codes. SRB materials have vastly different mechanical responses and failure mechanisms that occur over time and length scales spanning many orders of magnitude. By using space-time resolutions at cm and ms scales, and continuum descriptions of materials, nonlinear stress analyses of the entire rocket for normal and accident burn scenarios provide the over-arching framework for an array of subscale models/simulations. The very large-scale, entire rocket simulations (> 107 degrees of freedom) trigger an integrated suite of equally and often larger-scale micromechanical analyses (10 µm and 1 µs scales), which resolve the evolution of failure in constituent materials. The micromechanical models play an essential role in bridging length and time scales between the submicron simulations of material separation processes and realistic continuum models.
These geometrically complex models employ a mix of nonlinear shell and solid elements with classical constitutive models: visco-elastodynamic shell elements for filament wound composite cases, 3-D visco-elastodynamic elements for the solid propellant, 3-D thermo-elastodynamic elements for the nozzle, nonlinear visco-elastodynamic elements for the liner and viscoplastic shell, 3-D elements for metallic cases, joints and connectors. The constitutive models for these analyses are obtained from literature data for the case/joints/nozzle, and from subscale simulations of foam mechanics [1,2] for the liner and the mechanics of particulate composites for the solid propellant [3,4]. A mixed explicit/implicit approach, each with different time resolutions, is envisioned for these analyses: the explicit scheme facilitates coupling of the fluid/solid interface predicted by the CFD/combustion simulations; the implicit scheme accommodates the (comparatively) longer time scale of structural response during an SRB burn. Advancements in iterative and direct sparse solver technologies are key for the success of this implicit strategy, given the vast number of nodes needed to discretize the complex SRB geometry.
The whole rocket (stress/deformation) simulations provide a focus for the first generation codes with system integration hooks into the developing subscale and interface models. Through collaboration with fluids/combustion teams, the major effort here addresses the gas/combustion/solid propellant and gas/nozzle interfaces, where each component is characterized by its own time and length scales and its own kinematic representation (Lagrangian vs. Eulerian). These simulations must quantify the effects of uncertainties in geometry and material modeling simplifications. New developments achieved at UIUC for the sensitivity analysis of very large-scale finite element models [5,6] constitute a focal point for this effort. Instrumented ground and flight tests provide databases for validation of whole rocket, stress/deformation simulations.
Two strategies are envisioned to simulate failure processes in the four main structural components (case/joints, solid propellant, nozzle, and liner): (1) a multi-time, multi-length scale approach for intergranular cohesive failure (propellant) and brittle fracture (composites); (2) continuum damage mechanics (with embedded length scales) for metallic components that have finer microstructures. The new methodologies, algorithms, and codes developed here strongly complement efforts at LLNL and SNL aimed at improving the failure capabilities of legacy codes (NIKE, DYNA, PRONTO, JAC, etc.). Space constraints limit discussion here to a few key details of these strategies for the solid propellant and the metallic cases/joints/domes/nozzle.
Crack propagation occurs primarily by intergranular cohesive failure of the polymeric binder between the closely packed grains (typically 30 to 300 µm in size). Fig. 1 (above) illustrates the multiscale (length and time) framework proposed to capture effects of the granular response on the macroscale failure process of the solid propellant. At the length scale of individual grains (Fig. 1b), a 3-D Lagrangian volumetric/cohesive finite element scheme enables modeling of the spontaneous crack motion along complex branching paths [7,8]. The rate-dependent, nonlinear constitutive model used for the cohesive elements derives from subscale finite element analyses (Fig. 1c) involving a crack propagating between adjacent grains. Such simulations include features of the sub-grain microstructure (voids in the binder, adhesive vs. cohesive failure), and draw upon even more refined, discrete treatment of material at the molecular scale.
3-D contact mechanics plays a key role in the interaction between the granular fracture surfaces. Further complications at the levels of Fig. 1b-c arise from (1) dynamic loading of the macrocrack faces by pressure produced from remotely burning gases, and (2) state changes from solid to liquid then gas on these newly forming crack faces accompanied by severe thermal gradients in nearby material. These issues provide natural integration opportunities with other teams modeling combustion mechanics. Two competing effects thus drive the crack propagation process: the stress concentration ahead of the advancing crack fronts and the combustion process itself. Use of this 3-D, micromechanical model of intergranular crack propagation over a multi-cm3 volume surrounding the advancing crack front requires computational resources at terascale levels.
At the macroscale level (Fig. 1a), an adaptive space-time finite element scheme for the solid propellant provides the modeling flexibility of arbitrary Lagrangian-Eulerian techniques with the added possibility of continuous mesh adaptation in space and time [9,10]. This key capability can accurately resolve the topology changes associated with crack propagation obtained from the microscale analysis (Fig. 1b) and with the advancing combustion front. Rigorous error estimators drive the spatial mesh adaptation. Because time scales associated with the micro- and macro-level discretizations vary significantly, sub-cycling becomes necessary to couple the models in Fig. 1a-b.
Failure simulations of metallic components (cases/joints/nozzles/connectors of high-strength steel and Al alloys) address brittle/ductile dynamic crack propagation. Steel components pose a great risk for catastrophic failure when loading rates and temperatures trigger a fracture mode transition from ductile (void coalescence) to brittle (transgranular cleavage) [11]. Simulations to predict propagation for tens of mm employ a coupled ductile tearing-cleavage model based on computational cell elements each having sizes of 25 to 100 µm [12]. Advanced dilatant plasticity models for cell response: (1) provide robust descriptions of void growth, and (2) accommodate the competing effects of high-rate loading and thermal softening. Cell extinction creates new traction-free surfaces to extend cracks. Weibull-type parameters derived from the continuum stress field, as altered by prior crack propagation, yield the probabilities of mode transition to cleavage fracture [13,14]. Very large-scale, discrete models of individual cells, reflecting features of the ferrite matrix at less than 1 µm scales offer new opportunities to improve constitutive cell models [15]. Laboratory drop-tower testing of small fracture test specimens (cm in size) provides a basis for calibration-validation of these failure models.
[1] L. J. Gibson and M. F. Ashby. Cellular Solids - Structure and Properties. Pergamon Press, 1988.
[2] T. Herdtle and H. Aref. Numerical experiments on two-dimensional foam. J. Fluid Mech. 24I:233, 1992.
[3] B. R. Prasad, R. Nimmagadda and P. Sofronis. Creep strength of fiber and particulate composite materials: the effect of interface slip and diffusion. Mechs. of Matls., 23:1, 1996.
[4] B. R. Prasad, R. Nimmagadda and P. Sofronis. On the calculation of the matrix/reinforcement interface diffusion coefficient in diffusional relaxation of composite materials at high temperatures. Acta Metall., 44:2711, 1996.
[5] Z.-X. Wang, D. A. Tortorelli, and J. A. Dantzig. Sensitivity analysis and optimization of coupled thermal and flow problems with applications to contraction design. Int. J. Num. Meths. Fluids., 23:991, 1996.
[6] P. Michelaris, D. A. Tortorelli, and C. Vidal. Tangent operators and sensitivity formulations for transient nonlinear coupled problems with applications to elasto-plasticity. Int. J. Num. Meths. Engr., 37:14, 1994.
[7] G. T. Camacho and M. Ortiz. Computational modeling of impact damage in brittle materials. Int. J. Solids Structures, 33:2899, 1996
[8] X.-P. Xu and A. Needleman. Numerical simulation of fast crack growth in brittle solids. J. Mech. Phys. Solids, 42:1397, 1994.
[9] F. L. Carranza, B. Fang and R. B. Haber. An adaptive space-time finite element model for oxidation-driven fracture. to appear Comp. Meths. App. Mechs. & Engr., 1997.
[10] H.S. Lee and R. B. Haber. Eulerian-Lagrangian methods for crack growth in creeping materials. In Advanced Computational Methods for Material Modeling, D. J. Benson and R. A. Asaro, eds., AMD-Vol. 180 / PVP-Vol. 268:141, 1993.
[11] X. Gao, C. F. Shih, and V. Tvergaard and A. Needleman. Constraint effects on the ductile-brittle transition in small scale yielding. J. Mech. Phys. Solids, 44:1255, 1996.
[12] C. Ruggieri, T. L. Panontin, and R. H. Dodds. Numerical modeling of ductile crack growth in 3-D using computational cell elements. Int. J. Fracture, 1997, to appear.
[13] L. Xia and C. F. Shih. Ductile crack growth - III. Statistical aspects of cleavage fracture after tearing. J. Mech. Phys. Solids, 44:603, 1996.
[14] C. Ruggieri and R. H. Dodds. A transferability model for brittle fracture including constraint and ductile tearing effects: A probabilistic approach. Int. J. Fracture, 79:309, 1996.
[15] J. Faleskog and C. F. Shih. Micromechanics of coalescence - I. Synergistic effects of elasticity, plastic yielding and multi-size-scale voids. J. Mech. Phys. Solids, 45:21, 1997.
