Nonlinear structural modeling of solid propellants

Francis, E. C.; Thompson, Ren A.

doi:10.2514/6.1984-1290

Cited by 5 publications

(6 citation statements)

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“…3) Damage is incorporated in the constitutive equation using the "stress correction" approach of Swanson and Christensen 13 (also see Ref. 14), where a stress softening function is used to correct the stress response. 4) A continuum energy-based approach is used to determine the stress softeningdata from simple loading experiments.A suitable function that can account for the effect of different loading variables such as strain rate to t the stress softening data is determined.…”

Section: Nomenclature a Tmentioning

confidence: 99%

High Strain-Rate Constitutive Models for Solid Rocket Propellants

2002

Journal of Propulsion and Power

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A constitutive model that incorporates mechanical damage and nonlinear viscoelastic material response for solid composite rocket propellants has been developed for high strain-rate impact loading conditions. The numerical constants in this model could be related to the physics of the propellant and were obtained by nonlinear leastsquares tting of the data obtained from Hopkinson Bar experiments in the strain-rate range from 10 3 to 10 4 s ¡ 1 . Damage was taken into account using an approach based on correcting the viscoelastic function with a stress softening function. A simple method for calibrating the stress softening function using the recoverable strain energy density has been developed. This energy-based approach has the advantage of being able to capture damage more adequately and allows for bulk inelastic behavior. Predictions of the stress response of two different composite propellants for different loading conditions (temperature and strain rate) and histories (and, therefore, different damage levels) were made using the constitutive model. Good agreement between the predicted and experimentally measured stresses for strain levels up to 30-40% was obtained. The model was able to predict the stress response quite reasonably outside the temperature range used to develop the constitutive equation, but inside the range of the reduced strain-rate, indicating the validity of the time-temperature superposition principle for high strain-rate conditions. The model was also able to reproduce quite well the mechanical deformation (both in magnitude and shape of the stress-strain curve) of predamaged propellants. Nomenclature a T = time-temperature shift factor jd"=dt j = absolute strain rate E = modulus in initial linear elastic region of stress-strain curve f = viscoelastic stress G 00 = dynamic shear loss modulus g = stress softening function H r = hysteresis ratio m = exponent for strain softening/hardening n = exponent for strain-rate dependence T = temperature T g = glass transition temperature T 0 = reference temperature W i = input strain energy density W rc = recoverable strain energy density " = strain P " = strain raté = "pseudo," or arti cial, viscosity ¾ = stress

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Section: Nomenclature a Tmentioning

confidence: 99%

High Strain-Rate Constitutive Models for Solid Rocket Propellants

2002

Journal of Propulsion and Power

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“…He assumed that this parameter was a function of strain rate and recoverable deformation energy which he determined from loading/unloading data in uniaxial tension. Ho claims that his recoverable energy approach is better than the Swanson and Christensen (1983) and Francis and Thompson (1984) approaches in which damage was introduced in the constitutive law as a function of stress. Based on extensive experiments, Matheson and Nguyen (2005) developed a viscoelastic damage model to simulate the nonlinear behavior of a solid propellant material under different loading conditions.…”

Section: Introductionmentioning

confidence: 98%

“…Swanson and Christensen (1983) presented a constitutive model in which a strain softening function was used to describe the viscoelastic response of a high elongation solid propellant expressed in the form of a hereditary integral. Francis and Thompson (1984) used the same softening function approach as Swanson and Christensen (1983) in order to address complex loading and unloading situations, but their constitutive model requires a large number (four) of calibration experiments. Ö zu¨pek and Becker (1992) combined these two models to simulate finite-strain uniaxial response of a high elongation polyethyleneglycol/nitroglycerin (PEG/NG) solid ARTICLE IN PRESS oxidizer particle void fuel particle binder Fig.…”

Section: Introductionmentioning

confidence: 99%

Constitutive modeling of solid propellant materials with evolving microstructural damage

Aravas

Sofronis

2008

Journal of the Mechanics and Physics of Solids

102

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“…Strain rate and temperature history effects were incorporated by multiplying another internal state variable to the deviatoric part. Francis and Thompson [7] used the same softening function approach as Swanson and Christensen [6] for loading, unloading, relaxation and reloading situations. Simo [8] and Holzapfel [9] developed finite-strain viscoelastic constitutive model through the decomposition of strain energy into deviatoric and volumetric parts.…”

Section: Introductionmentioning

confidence: 99%

Hyperviscoelastic Constitutive Modelling of Solid Propellants with Damage and Compressibility

Kumar

Patel

Rao

et al. 2018

Propellants Explo Pyrotec

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Filled elastomers especially composite solid propellants demonstrate strain rate dependent, large deformation/large strain, thermo‐rheological, stress relaxation, stress softening due to microstructural damage and compressible constitutive behavior. This paper presents a micromechanism inspired framework capturing all the above mentioned features by combining both continuum formulation of hyperelasticity, statistical formulation of viscoelasticity, compressibility and damage. The mechanical response is decomposed into equilibrium and time dependent parts. The equilibrium and time dependent parts are further decomposed into dilational and deviatoric parts. Deviatoric parts are modelled using Mooney‐ Rivlin hyperelastic strain energy density functions. Compressibility is modelled by considering dilatational part of strain energy density as the function of the dilation with quadratic and quartic terms. The stress softening during cyclic loading (Mullins effect) due to microstructural damage is described by polynomial function of the current strain energy density and its previous maximum value. The predictions based on the proposed model are in good agreement with the experimental results.

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Nonlinear structural modeling of solid propellants

Cited by 5 publications

References 0 publications

High Strain-Rate Constitutive Models for Solid Rocket Propellants

High Strain-Rate Constitutive Models for Solid Rocket Propellants

Constitutive modeling of solid propellant materials with evolving microstructural damage

Hyperviscoelastic Constitutive Modelling of Solid Propellants with Damage and Compressibility

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