Parameterization of a rate-dependent model of shock-induced plasticity for copper, nickel, and aluminum

• Published in: International journal of plasticity Vol. 32-33; pp. 134 - 154
• Main Authors: Austin, Ryan A., McDowell, David L.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-05-2012; Elsevier
• Subjects: (A) Dislocations; (A) Shock waves; (B) Constitutive behavior; (B) Elastic–viscoplastic material; (B) Metallic material; Aluminum; Aluminum base alloys; Computer simulation; Condensed matter: structure, mechanical and thermal properties; Defects and impurities in crystals; microstructure; Dislocations; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Linear defects: dislocations, disclinations; Mathematical models; Nucleation; Parametrization; Physics; Shear strength; Solid mechanics; Static elasticity (thermoelasticity...); Stress waves; Structural and continuum mechanics; Structure of solids and liquids; crystallography; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); (A) Shock waves; (B) Metallic material; (B) Elastic–viscoplastic material; (B) Constitutive behavior; (A) Dislocations; Constitutive equation; Nucleation; Polycrystal; Elastic wave; Modeling; Shock wave; Dislocation; State variable; Inelasticity; Plasticity; Copper; Strain rate; Stress wave; Stress strain relation; Shear strength; (B) Elastic-viscoplastic material; Experimental study; Scaling law; Strain wave; Non invasive method; Viscoplasticity; Internal variable material
• ISSN: 0749-6419; 1879-2154
• DOI: 10.1016/j.ijplas.2011.11.002

► Constitutive model addresses the dynamic strength of metals under shock wave loading. ► Model flow stress depends on pressure, temperature, strain rate, and microstructure. ► Mobile and immobile dislocation densities are assigned as evolving internal state variables. ► Simulated velocity profiles and dynamic stress–strain curves are in agreement with experiments. ► The model reproduces the Swegle–Grady scaling law for strain rates up to 1010s−1.
A mechanistic model of shock-wave-induced viscoplasticity is parameterized for three polycrystalline metals: Cu, Ni, and Al. The model is also extended to higher stress wave amplitudes by incorporating homogeneous dislocation nucleation within the constitutive framework. Steady shock waves are simulated to demonstrate the model and compare results to experimental data. Stress wave amplitudes of up to 30GPa have been simulated in each metal; these stress waves generate strain rates of up to ∼1010s−1 in the shock front. Model results compare favorably with experimental velocity profiles, dynamic stress–strain curves, the Swegle-Grady scaling law, and non-invasive measurements of shear strength in the shocked state. Furthermore, simulated stress-strain-rate profiles exhibit points of self-intersection (loops) because the mobile and immobile dislocation densities have been assigned as internal state variables. Such loops, which have been observed in experiments, are not captured by flow functions that are based on a single monotonically-increasing internal state variable. Finally, the model of 6061-T6 Al alloy is revisited to ammend a prior conclusion regarding shear strength in the shocked state and the onset of homogeneous dislocation nucleation.